Using C# for Graphics and GUIs Handout #2

Size: px
Start display at page:

Download "Using C# for Graphics and GUIs Handout #2"

Transcription

1 Using C# for Graphics and GUIs Handout #2 Learning Objectives: Review Math methods C# Arras Drawing Rectangles Getting height and width of window Coloring with FromArgb() Sierpinski Triangle 1

2 Math Methods and Constants in C# To use methods from math, such as sin and cos, use Math. Methods use parentheses, constants don t. Eamples: =Math.Cos(); A=2.0*Math.PI*r*r; 2

3 C# Arras Arras in C# are somewhat like Vectors in C++. You can size them with variables and the have functions associated with them. Declaring Arras: 1-D integer arra declaration: int[ ] = new int[5]; 2-D Rectangular integer arra declaration: int[, ] = new int[5, 4]; Using 1-D arras = same as C++, e.g. [2]=3; Using 2-D rectangular arras: [1, 3] = 4; Use.Length instead of.size() For 2-D:.Length gives number of rows.longlength gives total number of elements 3

4 C# Structures You can make structures in C# just like in C. The differences are that ou need to use the keword public when declaring our fields and no semi-colon at the end: Eample: struct Point { public int, ; } You can put this at the top of our namespace or above it. Use this structure just like ou did in C. Eample Using a point structure: Point p; p. = 5; p. = 10; 4

5 Drawing Rectangles Note: This is available because at the top we have: using namespace Sstem.Drawing 1. Create an object of the Graphics class to tell where ou want our graphics: Graphics g=this.creategraphics(); //do this onl once //g is the object name, this refers to the form itself //if ou wanted graphics in a picturebo (ou d use something //like: Graphics gp = picturebo1.creategraphics() 2. To fill in objects with color, first declare a SolidBrush: SolidBrush sbblue = new SolidBrush(Color.Blue); 3. To create a filled rectangle on g (the form s graphics object): g.fillrectangle(sbblue,0,0,100,75) //creates a blue rectangle that //starts at piel 0,0 and is 100 piels wide and 75 piels high. Tr it. Draw a rectangle when ou click a button. If ou have time, draw two rectangles when ou hit the button. 5

6 Note: For the Sierpinski triangles (the net HW assignment), we want to fill in piels. We can do this with rectangles that are 1 piel wide and 1 piel high. Form s height and width You can use the form s height and width to calculate where to put the Sierpinski triangle points. To get the height, use: this.height To get the width, use: this.width Tr this: Use this.height and this.width to position our rectangle s upper left corner at the center of the form. If ou have time, center the rectangle on the form. 6

7 Random Numbers in C# Just one of these: (declares a random number generator object) Random r = new Random( ); To get a random integer from 0 to 5: i = r.net(6); //this is just like i = rand()%6 To get another random integer from 0 to 9: i = r.net(10) 7

8 Coloring with FromArgb When we wanted to color a rectangle blue, we used: Brush sbblue = new SolidBrush(Color.Blue); You can specif the eact color b replacing Color.Blue with: Color.FromArgb(ired,igreen,iblue) ired, igreen, and iblue are integers from 0 to 255 ired, igreen, and iblue can be epressions that depend on other variables. Note: You can eperiment with different rgb values and colors in the Microsoft program Paint Tr it Color our rectangle using FromArgb 8

9 Sierpinski Triangle Start with the three corner points of an equilateral triangle and label them 0, 1, and 2 Choose a random number from 0 to 2 and start at that point Find another random number from 0 to 2 and move ½ wa toward that point, leaving a dot where ou land. Sa I got a 1, then 0 put a dot ½ wa between 0 and 1. Then 1 put a dot ½ wa between last dot and 1. Then 2, etc 0 What do ou think I end up with? See program 2 1 9

10 We ll use piels instead of dots A piel is the smallest area ou can access on a screen and window sizes are normall defined b their height and width in piels. (A piel is a ver small square.) Your drawing area will start at 0,0 in the upper left corner: 0,0 10

11 How do we find the three corner pt 1 pt 2 piels? r pt 0 How would ou find i with four points? Divide b four instead of 3 and find one more = 0 1 = 2 = = r =r(cos( 0 )) 1 = r(cos( 1 )) 2 = r(cos( 2 )) 0 = 0 =r(sin( 0 )) 1 = r(sin( 1 )) 2 = r(sin( 2 )) 11

12 Rotate the triangle -90 = - /2 rad pt = 1 = 2 = Wh did I make this triangle upside down? goes from top to bottom on our 12 screen

13 How do ou find ½ wa to the net point? pt 2 pt 1 pt 0 Current position 0, 0 go ½ wa to 1, 1 new old 2 corner new old 2 corner 13

Double Integrals in Polar Coordinates

Double Integrals in Polar Coordinates Double Integrals in Polar Coordinates. A flat plate is in the shape of the region in the first quadrant ling between the circles + and +. The densit of the plate at point, is + kilograms per square meter

More information

The Marching Cougars Lesson 9-1 Transformations

The Marching Cougars Lesson 9-1 Transformations The Marching Cougars Lesson 9-1 Learning Targets: Perform transformations on and off the coordinate plane. Identif characteristics of transformations that are rigid motions and characteristics of transformations

More information

Math 26: Fall (part 1) The Unit Circle: Cosine and Sine (Evaluating Cosine and Sine, and The Pythagorean Identity)

Math 26: Fall (part 1) The Unit Circle: Cosine and Sine (Evaluating Cosine and Sine, and The Pythagorean Identity) Math : Fall 0 0. (part ) The Unit Circle: Cosine and Sine (Evaluating Cosine and Sine, and The Pthagorean Identit) Cosine and Sine Angle θ standard position, P denotes point where the terminal side of

More information

More Coordinate Graphs. How do we find coordinates on the graph?

More Coordinate Graphs. How do we find coordinates on the graph? Lesson Problem Solving: More Coordinate Graphs Problem Solving: More Coordinate Graphs How do we find coordinates on the graph? We use coordinates to find where the dot goes on the coordinate graph. From

More information

Lesson 11 Skills Maintenance. Activity 1. Model. The addition problem is = 4. The subtraction problem is 5 9 = 4.

Lesson 11 Skills Maintenance. Activity 1. Model. The addition problem is = 4. The subtraction problem is 5 9 = 4. Lesson Skills Maintenance Lesson Planner Vocabular Development -coordinate -coordinate point of origin Skills Maintenance ddition and Subtraction of Positive and Negative Integers Problem Solving: We look

More information

M O T I O N A N D D R A W I N G

M O T I O N A N D D R A W I N G 2 M O T I O N A N D D R A W I N G Now that ou know our wa around the interface, ou re read to use more of Scratch s programming tools. In this chapter, ou ll do the following: Eplore Scratch s motion and

More information

Transformations in the Plane - Activity 1 Reflections in axes and an oblique line.

Transformations in the Plane - Activity 1 Reflections in axes and an oblique line. Name: Class: p 5 Maths Helper Plus Resource Set. Copyright 00 Bruce A. Vaughan, Teachers Choice Software Transformations in the Plane - Activity Reflections in axes and an oblique line. ) On the diagram

More information

CISC 1600 Lecture 3.1 Introduction to Processing

CISC 1600 Lecture 3.1 Introduction to Processing CISC 1600 Lecture 3.1 Introduction to Processing Topics: Example sketches Drawing functions in Processing Colors in Processing General Processing syntax Processing is for sketching Designed to allow artists

More information

Math 1050 Lab Activity: Graphing Transformations

Math 1050 Lab Activity: Graphing Transformations Math 00 Lab Activit: Graphing Transformations Name: We'll focus on quadratic functions to eplore graphing transformations. A quadratic function is a second degree polnomial function. There are two common

More information

Lesson 21: Surface Area

Lesson 21: Surface Area Lesson 21: Surface Area Classwork Opening Exercise: Surface Area of a Right Rectangular Prism On the provided grid, draw a net representing the surfaces of the right rectangular prism (assume each grid

More information

LECTURE 6: CROSS VALIDATION

LECTURE 6: CROSS VALIDATION LECTURE 6: CROSS VALIDATION CSCI 4352 Machine Learning Dongchul Kim, Ph.D. Department of Computer Science A Regression Problem Given a data set, how can we evaluate our (linear) model? Cross Validation

More information

Integrated Algebra A Notes/Homework Packet 9

Integrated Algebra A Notes/Homework Packet 9 Name Date Integrated Algebra A Notes/Homework Packet 9 Lesson Homework Graph Using the Calculator HW # Graph with Slope/Intercept Method HW # Graph with Slope/Intercept Method-Continued HW #3 Review Put

More information

Surface Area and Volume

Surface Area and Volume 15 CHAPTER Surface Area and Volume Lesson 15.1 Building Solids Using Unit Cubes How many unit cubes are used to build each solid? 1. 2. unit cubes unit cubes Extra Practice 5B 115 3. unit cubes 4. 5. unit

More information

Uses of Transformations. 2D transformations Homogeneous coordinates. Transformations. Transformations. Transformations. Transformations and matrices

Uses of Transformations. 2D transformations Homogeneous coordinates. Transformations. Transformations. Transformations. Transformations and matrices Uses of Transformations 2D transformations Homogeneous coordinates odeling: position and resie parts of a comple model; Viewing: define and position the virtual camera Animation: define how objects move/change

More information

Special Products on Factoring

Special Products on Factoring Special Products on Factoring What Is This Module About? This module is a continuation of the module on polnomials. In the module entitled Studing Polnomials, ou learned what polnomials are as well as

More information

20 Calculus and Structures

20 Calculus and Structures 0 Calculus and Structures CHAPTER FUNCTIONS Calculus and Structures Copright LESSON FUNCTIONS. FUNCTIONS A function f is a relationship between an input and an output and a set of instructions as to how

More information

Lesson 12: Sine 5 = 15 3

Lesson 12: Sine 5 = 15 3 Lesson 12: Sine How did ou do on that last worksheet? Is finding the opposite side and adjacent side of an angle super-duper eas for ou now? Good, now I can show ou wh I wanted ou to learn that first.

More information

Today s class. Geometric objects and transformations. Informationsteknologi. Wednesday, November 7, 2007 Computer Graphics - Class 5 1

Today s class. Geometric objects and transformations. Informationsteknologi. Wednesday, November 7, 2007 Computer Graphics - Class 5 1 Toda s class Geometric objects and transformations Wednesda, November 7, 27 Computer Graphics - Class 5 Vector operations Review of vector operations needed for working in computer graphics adding two

More information

Transforming Coordinates

Transforming Coordinates # Transforming Coordinates The drawing window in man computer geometr programs is a coordinate grid. You make designs b specifing the endpoints of line segments. When ou transform a design, the coordinates

More information

Nets and Drawings for Visualizing Geometry. Unit 1 Lesson 1

Nets and Drawings for Visualizing Geometry. Unit 1 Lesson 1 Nets and Drawings for Visualizing Geometry Unit 1 Lesson 1 Students will be able to: Represent three-dimensional figures using nets. Make isometric and orthographic drawings. Key Vocabulary: Net Isometric

More information

Flux Integrals. Solution. We want to visualize the surface together with the vector field. Here s a picture of exactly that:

Flux Integrals. Solution. We want to visualize the surface together with the vector field. Here s a picture of exactly that: Flu Integrals The pictures for problems # - #4 are on the last page.. Let s orient each of the three pictured surfaces so that the light side is considered to be the positie side. Decide whether each of

More information

Intermediate Algebra. Gregg Waterman Oregon Institute of Technology

Intermediate Algebra. Gregg Waterman Oregon Institute of Technology Intermediate Algebra Gregg Waterman Oregon Institute of Technolog c 2017 Gregg Waterman This work is licensed under the Creative Commons Attribution 4.0 International license. The essence of the license

More information

Modeling Transformations

Modeling Transformations Modeling Transformations Michael Kazhdan (601.457/657) HB Ch. 5 FvDFH Ch. 5 Announcement Assignment 2 has been posted: Due: 10/24 ASAP: Download the code and make sure it compiles» On windows: just build

More information

Translations, Reflections, and Rotations

Translations, Reflections, and Rotations Translations, Reflections, and Rotations The Marching Cougars Lesson 9-1 Transformations Learning Targets: Perform transformations on and off the coordinate plane. Identif characteristics of transformations

More information

Modeling Transformations

Modeling Transformations Modeling Transformations Michael Kazhdan (601.457/657) HB Ch. 5 FvDFH Ch. 5 Overview Ra-Tracing so far Modeling transformations Ra Tracing Image RaTrace(Camera camera, Scene scene, int width, int heigh,

More information

Prof. Feng Liu. Fall /25/2018

Prof. Feng Liu. Fall /25/2018 Prof. Feng Liu Fall 08 http://www.cs.pd.edu/~fliu/courses/cs7/ 0/5/08 Last time Clipping Toda Rasterization In-class Mid-term November Close-book eam Notes on page of A or Letter size paper Where We Stand

More information

Graphing Calculator Graphing with the TI-86

Graphing Calculator Graphing with the TI-86 Graphing Calculator Graphing with the TI-86 I. Introduction The TI-86 has fift kes, man of which perform multiple functions when used in combination. Each ke has a smbol printed on its face. When a ke

More information

Matrix Representations

Matrix Representations CONDENSED LESSON 6. Matri Representations In this lesson, ou Represent closed sstems with transition diagrams and transition matrices Use matrices to organize information Sandra works at a da-care center.

More information

Determining the 2d transformation that brings one image into alignment (registers it) with another. And

Determining the 2d transformation that brings one image into alignment (registers it) with another. And Last two lectures: Representing an image as a weighted combination of other images. Toda: A different kind of coordinate sstem change. Solving the biggest problem in using eigenfaces? Toda Recognition

More information

Aim: How do we find the volume of a figure with a given base? Get Ready: The region R is bounded by the curves. y = x 2 + 1

Aim: How do we find the volume of a figure with a given base? Get Ready: The region R is bounded by the curves. y = x 2 + 1 Get Ready: The region R is bounded by the curves y = x 2 + 1 y = x + 3. a. Find the area of region R. b. The region R is revolved around the horizontal line y = 1. Find the volume of the solid formed.

More information

Week 3. Topic 5 Asymptotes

Week 3. Topic 5 Asymptotes Week 3 Topic 5 Asmptotes Week 3 Topic 5 Asmptotes Introduction One of the strangest features of a graph is an asmptote. The come in three flavors: vertical, horizontal, and slant (also called oblique).

More information

Week 10. Topic 1 Polynomial Functions

Week 10. Topic 1 Polynomial Functions Week 10 Topic 1 Polnomial Functions 1 Week 10 Topic 1 Polnomial Functions Reading Polnomial functions result from adding power functions 1 together. Their graphs can be ver complicated, so the come up

More information

Unit 4 Trigonometry. Study Notes 1 Right Triangle Trigonometry (Section 8.1)

Unit 4 Trigonometry. Study Notes 1 Right Triangle Trigonometry (Section 8.1) Unit 4 Trigonometr Stud Notes 1 Right Triangle Trigonometr (Section 8.1) Objective: Evaluate trigonometric functions of acute angles. Use a calculator to evaluate trigonometric functions. Use trigonometric

More information

The Menger Sponge in Google SketchUp

The Menger Sponge in Google SketchUp The Sierpinsky Carpet (shown below on the left) is a 2D fractal made from squares repeatedly divided into nine smaller squares. The Menger Sponge (shown below on the right) is the 3D version of this fractal.

More information

TABLE OF CONTENTS. Worksheets Lesson 1 Worksheet Introduction to Geometry 41 Lesson 2 Worksheet Naming Plane and Solid Shapes.. 44

TABLE OF CONTENTS. Worksheets Lesson 1 Worksheet Introduction to Geometry 41 Lesson 2 Worksheet Naming Plane and Solid Shapes.. 44 Acknowledgement: A+ TutorSoft would like to thank all the individuals who helped research, write, develop, edit, and launch our MATH Curriculum products. Countless weeks, years, and months have been devoted

More information

The Cartesian plane 15B

The Cartesian plane 15B Weblink attleship Game e A bishop can move diagonall an number of (unoccupied) squares at a time. omplete the following sentence: With its net move, the bishop at b could capture the........ (name the

More information

Online Homework Hints and Help Extra Practice

Online Homework Hints and Help Extra Practice Evaluate: Homework and Practice Use a graphing calculator to graph the polnomial function. Then use the graph to determine the function s domain, range, and end behavior. (Use interval notation for the

More information

Transformations of Functions. 1. Shifting, reflecting, and stretching graphs Symmetry of functions and equations

Transformations of Functions. 1. Shifting, reflecting, and stretching graphs Symmetry of functions and equations Chapter Transformations of Functions TOPICS.5.. Shifting, reflecting, and stretching graphs Smmetr of functions and equations TOPIC Horizontal Shifting/ Translation Horizontal Shifting/ Translation Shifting,

More information

Three Dimensional Figures. TeacherTwins 2015

Three Dimensional Figures. TeacherTwins 2015 Three Dimensional Figures TeacherTwins 2015 Warm Up What is a 2 dimensional figure? What is a three dimensional figure? Draw a picture of each. Using the nets provided, make the following three dimensional

More information

Investigation Free Fall

Investigation Free Fall Investigation Free Fall Name Period Date You will need: a motion sensor, a small pillow or other soft object What function models the height of an object falling due to the force of gravit? Use a motion

More information

The surface area of a solid figure is the sum of the areas of its surfaces. To help you see all the surfaces of a solid figure, you can use a net.

The surface area of a solid figure is the sum of the areas of its surfaces. To help you see all the surfaces of a solid figure, you can use a net. The surface area of a solid figure is the sum of the areas of its surfaces. To help you see all the surfaces of a solid figure, you can use a net. A net is the pattern made when the surface of a solid

More information

The figures below are all prisms. The bases of these prisms are shaded, and the height (altitude) of each prism marked by a dashed line:

The figures below are all prisms. The bases of these prisms are shaded, and the height (altitude) of each prism marked by a dashed line: Prisms Most of the solids you ll see on the Math IIC test are prisms or variations on prisms. A prism is defined as a geometric solid with two congruent bases that lie in parallel planes. You can create

More information

WHOLE NUMBER AND DECIMAL OPERATIONS

WHOLE NUMBER AND DECIMAL OPERATIONS WHOLE NUMBER AND DECIMAL OPERATIONS Whole Number Place Value : 5,854,902 = Ten thousands thousands millions Hundred thousands Ten thousands Adding & Subtracting Decimals : Line up the decimals vertically.

More information

R cm T 60 K

R cm T 60 K Mathematics(NSC)/Grade 11/ P 19 Eemplar Grade 11 Mathematics: Question Paper MARKS: 150 TIME: 3hours QUESTION 1 1.1 A triangle is drawn with vertices A (0;) ; B (4;5) and C (4;-4). 1.1.1 Find the length

More information

What and Why Transformations?

What and Why Transformations? 2D transformations What and Wh Transformations? What? : The geometrical changes of an object from a current state to modified state. Changing an object s position (translation), orientation (rotation)

More information

Discovering. Algebra. An Investigative Approach. Condensed Lessons for Make-up Work

Discovering. Algebra. An Investigative Approach. Condensed Lessons for Make-up Work Discovering Algebra An Investigative Approach Condensed Lessons for Make-up Work CONDENSED L E S S O N 0. The Same yet Smaller Previous In this lesson you will apply a recursive rule to create a fractal

More information

g(x) h(x) f (x) = Examples sin x +1 tan x!

g(x) h(x) f (x) = Examples sin x +1 tan x! Lecture 4-5A: An Introduction to Rational Functions A Rational Function f () is epressed as a fraction with a functiong() in the numerator and a function h() in the denominator. f () = g() h() Eamples

More information

1. (10 pts) Order the following three images by how much memory they occupy:

1. (10 pts) Order the following three images by how much memory they occupy: CS 47 Prelim Tuesday, February 25, 2003 Problem : Raster images (5 pts). (0 pts) Order the following three images by how much memory they occupy: A. a 2048 by 2048 binary image B. a 024 by 024 grayscale

More information

My Favourite Problem No.5 Solution

My Favourite Problem No.5 Solution My Favourite Problem No.5 Solution The wonderful thing about this problem is that it can be solved in a number of ways. ) Solution by dissection So far, we have this construction. The trick here is to

More information

An Introduction to Processing

An Introduction to Processing An Introduction to Processing Creating static drawings Produced by: Mairead Meagher Dr. Siobhán Drohan Department of Computing and Mathematics http://www.wit.ie/ Topics list Coordinate System in Computing.

More information

Pre-Algebra Notes Unit 8: Graphs and Functions

Pre-Algebra Notes Unit 8: Graphs and Functions Pre-Algebra Notes Unit 8: Graphs and Functions The Coordinate Plane A coordinate plane is formed b the intersection of a horizontal number line called the -ais and a vertical number line called the -ais.

More information

(0, 4) Figure 12. x + 3. d = c. = b. Figure 13

(0, 4) Figure 12. x + 3. d = c. = b. Figure 13 80 CHAPTER EQUATIONS AND INEQUALITIES Plot both points, and draw a line passing through them as in Figure. Tr It # _, 0 Figure Find the intercepts of the equation and sketch the graph: = _ +. (0, (This

More information

5.2 Graphing Polynomial Functions

5.2 Graphing Polynomial Functions Name Class Date 5.2 Graphing Polnomial Functions Essential Question: How do ou sketch the graph of a polnomial function in intercept form? Eplore 1 Investigating the End Behavior of the Graphs of Simple

More information

Name Date. using the vector 1, 4. Graph ABC. and its image. + to find the image

Name Date. using the vector 1, 4. Graph ABC. and its image. + to find the image _.1 ractice 1. Name the vector and write its component form. K J. The vertices of, 3, 1,, and 0, 1. Translate using the vector 1,. Graph and its image. are ( ) ( ) ( ) 3. Find the component form of the

More information

Section 4.2 Graphing Lines

Section 4.2 Graphing Lines Section. Graphing Lines Objectives In this section, ou will learn to: To successfull complete this section, ou need to understand: Identif collinear points. The order of operations (1.) Graph the line

More information

Programming Language. Functions. Eng. Anis Nazer First Semester

Programming Language. Functions. Eng. Anis Nazer First Semester Programming Language Functions Eng. Anis Nazer First Semester 2016-2017 Definitions Function : a set of statements that are written once, and can be executed upon request Functions are separate entities

More information

turn counterclockwise from the positive x-axis. However, we could equally well get to this point by a 3 4 turn clockwise, giving (r, θ) = (1, 3π 2

turn counterclockwise from the positive x-axis. However, we could equally well get to this point by a 3 4 turn clockwise, giving (r, θ) = (1, 3π 2 Math 133 Polar Coordinates Stewart 10.3/I,II Points in polar coordinates. The first and greatest achievement of modern mathematics was Descartes description of geometric objects b numbers, using a sstem

More information

PROBLEM SOLVING WITH EXPONENTIAL FUNCTIONS

PROBLEM SOLVING WITH EXPONENTIAL FUNCTIONS Topic 21: Problem solving with eponential functions 323 PROBLEM SOLVING WITH EXPONENTIAL FUNCTIONS Lesson 21.1 Finding function rules from graphs 21.1 OPENER 1. Plot the points from the table onto the

More information

CS F-07 Objects in 2D 1

CS F-07 Objects in 2D 1 CS420-2010F-07 Objects in 2D 1 07-0: Representing Polgons We want to represent a simple polgon Triangle, rectangle, square, etc Assume for the moment our game onl uses these simple shapes No curves for

More information

Solution Guide for Chapter 20

Solution Guide for Chapter 20 Solution Guide for Chapter 0 Here are the solutions for the Doing the Math exercises in Girls Get Curves! DTM from p. 351-35. In the diagram SLICE, LC and IE are altitudes of the triangle!sci. L I If SI

More information

Mathematics Success Grade 6

Mathematics Success Grade 6 Mathematics Success Grade 6 T683 [OBJECTIVE] The student will determine the volume of rectangular prisms with fractional edge lengths and solve problems in mathematical and real-world situations. [PREREQUISITE

More information

1 Getting started with Processing

1 Getting started with Processing cis3.5, spring 2009, lab II.1 / prof sklar. 1 Getting started with Processing Processing is a sketch programming tool designed for use by non-technical people (e.g., artists, designers, musicians). For

More information

0 COORDINATE GEOMETRY

0 COORDINATE GEOMETRY 0 COORDINATE GEOMETRY Coordinate Geometr 0-1 Equations of Lines 0- Parallel and Perpendicular Lines 0- Intersecting Lines 0- Midpoints, Distance Formula, Segment Lengths 0- Equations of Circles 0-6 Problem

More information

Math-2 Lesson 6-3: Area of: Triangles, rectangles, circles and Surface Area of Pyramids

Math-2 Lesson 6-3: Area of: Triangles, rectangles, circles and Surface Area of Pyramids Math- Lesson 6-3: rea of: Triangles, rectangles, circles and Surface rea of Pyramids SM: Lesson 6-3 (rea) For the following geometric shapes, how would you answer the question; how big is it? Describe

More information

Developing Conceptual Understanding of Number. Set H: Coordinate Geometry

Developing Conceptual Understanding of Number. Set H: Coordinate Geometry Developing Conceptual Understanding of Number Set H: Coordinate Geometr Carole Bilk cbilk@gov.mb.ca Wane Watt wwatt@mts.net Vocabular -ais -ais -coordinate -coordinate Notes Coordinate Geometr 1 coordinate

More information

L3 Rigid Motion Transformations 3.1 Sequences of Transformations Per Date

L3 Rigid Motion Transformations 3.1 Sequences of Transformations Per Date 3.1 Sequences of Transformations Per Date Pre-Assessment Which of the following could represent a translation using the rule T (, ) = (, + 4), followed b a reflection over the given line? (The pre-image

More information

Graphing square root functions. What would be the base graph for the square root function? What is the table of values?

Graphing square root functions. What would be the base graph for the square root function? What is the table of values? Unit 3 (Chapter 2) Radical Functions (Square Root Functions Sketch graphs of radical functions b appling translations, stretches and reflections to the graph of Analze transformations to identif the of

More information

Lab 2: Booleans, Strings, Random Numbers, Recursion, Variables, Input function

Lab 2: Booleans, Strings, Random Numbers, Recursion, Variables, Input function Lab 2: Booleans, Strings, Random Numbers, Recursion, Variables, Input function Due: Mar25 (Note that this is a 2-week lab) This lab must be done using paired partners. You should choose a different partner

More information

Cross-validation for detecting and preventing overfitting

Cross-validation for detecting and preventing overfitting Cross-validation for detecting and preventing overfitting Andrew W. Moore/Anna Goldenberg School of Computer Science Carnegie Mellon Universit Copright 2001, Andrew W. Moore Apr 1st, 2004 Want to learn

More information

LESSON 3.1 INTRODUCTION TO GRAPHING

LESSON 3.1 INTRODUCTION TO GRAPHING LESSON 3.1 INTRODUCTION TO GRAPHING LESSON 3.1 INTRODUCTION TO GRAPHING 137 OVERVIEW Here s what ou ll learn in this lesson: Plotting Points a. The -plane b. The -ais and -ais c. The origin d. Ordered

More information

Surface Area and Volume

Surface Area and Volume Surface Area and Volume Day 1 - Surface Area of Prisms Surface Area = The total area of the surface of a three-dimensional object (Or think of it as the amount of paper you ll need to wrap the shape.)

More information

About Finish Line New Jersey Math 5

About Finish Line New Jersey Math 5 Table of COntents About Finish Line New Jerse Math Unit : Big Ideas from Grade Lesson.NBT., Multipling and Dividing Whole Numbers [connects to.nbt., ] Lesson.NF., Understanding Decimals [connects to.nbt..a,

More information

Answers Investigation 4

Answers Investigation 4 Answers Investigation Applications. a. At seconds, the flare will have traveled to a maimum height of 00 ft. b. The flare will hit the water when the height is 0 ft, which will occur at 0 seconds. c. In

More information

AP Calculus. Areas and Volumes. Student Handout

AP Calculus. Areas and Volumes. Student Handout AP Calculus Areas and Volumes Student Handout 016-017 EDITION Use the following link or scan the QR code to complete the evaluation for the Study Session https://www.surveymonkey.com/r/s_sss Copyright

More information

Rotate. A bicycle wheel can rotate clockwise or counterclockwise. ACTIVITY: Three Basic Ways to Move Things

Rotate. A bicycle wheel can rotate clockwise or counterclockwise. ACTIVITY: Three Basic Ways to Move Things . Rotations object in a plane? What are the three basic was to move an Rotate A biccle wheel can rotate clockwise or counterclockwise. 0 0 0 9 9 9 8 8 8 7 6 7 6 7 6 ACTIVITY: Three Basic Was to Move Things

More information

Creating objects TOPIC 3 INTRODUCTION TO PROGRAMMING. Making things to program with.

Creating objects TOPIC 3 INTRODUCTION TO PROGRAMMING. Making things to program with. 1 Outline TOPIC 3 INTRODUCTION TO PROGRAMMING Notes adapted from Introduction to Computing and Programming with Java: A Multimedia Approach by M. Guzdial and B. Ericson, and instructor materials prepared

More information

Enhanced Instructional Transition Guide

Enhanced Instructional Transition Guide Enhanced Instructional Transition Guide / Unit 04: Suggested Duration: 6 das Unit 04: Geometr: Coordinate Plane, Graphing Transformations, and Perspectives (9 das) Possible Lesson 0 (6 das) Possible Lesson

More information

Draw and Classify 3-Dimensional Figures

Draw and Classify 3-Dimensional Figures Introduction to Three-Dimensional Figures Draw and Classify 3-Dimensional Figures Identify various three-dimensional figures. Course 2 Introduction to Three-Dimensional Figures Insert Lesson Title Here

More information

Think About. Unit 5 Lesson 3. Investigation. This Situation. Name: a Where do you think the origin of a coordinate system was placed in creating this

Think About. Unit 5 Lesson 3. Investigation. This Situation. Name: a Where do you think the origin of a coordinate system was placed in creating this Think About This Situation Unit 5 Lesson 3 Investigation 1 Name: Eamine how the sequence of images changes from frame to frame. a Where do ou think the origin of a coordinate sstem was placed in creating

More information

Outline. Turtles. Creating objects. Turtles. Turtles in Java 1/27/2011 TOPIC 3 INTRODUCTION TO PROGRAMMING. Making things to program with.

Outline. Turtles. Creating objects. Turtles. Turtles in Java 1/27/2011 TOPIC 3 INTRODUCTION TO PROGRAMMING. Making things to program with. 1 Outline 2 TOPIC 3 INTRODUCTION TO PROGRAMMING Notes adapted from Introduction to Computing and Programming with Java: A Multimedia Approach by M. Guzdial and B. Ericson, and instructor materials prepared

More information

C1M0 Introduction to Maple Assignment Format C1M1 C1M1 Midn John Doe Section 1234 Beginning Maple Syntax any

C1M0 Introduction to Maple Assignment Format C1M1 C1M1 Midn John Doe Section 1234 Beginning Maple Syntax any CM0 Introduction to Maple Our discussion will focus on Maple 6, which was developed by Waterloo Maple Inc. in Waterloo, Ontario, Canada. Quoting from the Maple 6 Learning Guide, Maple is a Symbolic Computation

More information

Guided Problem Solving

Guided Problem Solving -1 Guided Problem Solving GPS Student Page 57, Exercises 1 1: Match each rule with the correct translation. A. (x, y) (x, y 1 ) I. P(, 1) P (3, ) B. (x, y) (x 1 3, y) II. Q(3, 0) Q (3, ) C. (x, y) (x 1,

More information

ACTIVITY: Forming the Entire Coordinate Plane

ACTIVITY: Forming the Entire Coordinate Plane .5 The Coordinate Plane How can ou graph and locate points that contain negative numbers in a coordinate plane? You have alread graphed points and polgons in one part of the coordinate plane. In Activit,

More information

6 th Grade Math Cylinder Task. c) Draw a net (pattern) for the manufacturer to use to make the can.

6 th Grade Math Cylinder Task. c) Draw a net (pattern) for the manufacturer to use to make the can. 6 th Grade Math a) Explain what is meant by surface area. What steps would you take to find the surface area of a cylinder? b) One of the major expenses in manufacturing a can is the amount of metal that

More information

An Introduction to Maple This lab is adapted from a lab created by Bob Milnikel.

An Introduction to Maple This lab is adapted from a lab created by Bob Milnikel. Some quick tips for getting started with Maple: An Introduction to Maple This lab is adapted from a lab created by Bob Milnikel. [Even before we start, take note of the distinction between Tet mode and

More information

In this lecture we will briefly examine a few new controls, introduce the concept of scope, random numbers, and drawing simple graphics.

In this lecture we will briefly examine a few new controls, introduce the concept of scope, random numbers, and drawing simple graphics. Additional Controls, Scope, Random Numbers, and Graphics CS109 In this lecture we will briefly examine a few new controls, introduce the concept of scope, random numbers, and drawing simple graphics. Combo

More information

Lecture 7. CS4442/9542b: Artificial Intelligence II Prof. Olga Veksler. Outline. Machine Learning: Cross Validation. Performance evaluation methods

Lecture 7. CS4442/9542b: Artificial Intelligence II Prof. Olga Veksler. Outline. Machine Learning: Cross Validation. Performance evaluation methods CS4442/9542b: Artificial Intelligence II Prof. Olga Veksler Lecture 7 Machine Learning: Cross Validation Outline Performance evaluation methods test/train sets cross-validation k-fold Leave-one-out 1 A

More information

Lesson 1. Unit 2 Practice Problems. Problem 2. Problem 1. Solution 1, 4, 5. Solution. Problem 3

Lesson 1. Unit 2 Practice Problems. Problem 2. Problem 1. Solution 1, 4, 5. Solution. Problem 3 Unit 2 Practice Problems Lesson 1 Problem 1 Rectangle measures 12 cm by 3 cm. Rectangle is a scaled copy of Rectangle. Select all of the measurement pairs that could be the dimensions of Rectangle. 1.

More information

Grade 6 Math Circles. Shapeshifting

Grade 6 Math Circles. Shapeshifting Faculty of Mathematics Waterloo, Ontario N2L 3G1 Plotting Grade 6 Math Circles October 24/25, 2017 Shapeshifting Before we begin today, we are going to quickly go over how to plot points. Centre for Education

More information

The Quadratic function f(x) = x 2 2x 3. y y = x 2 2x 3. We will now begin to study the graphs of the trig functions, y = sinx, y = cosx and y = tanx.

The Quadratic function f(x) = x 2 2x 3. y y = x 2 2x 3. We will now begin to study the graphs of the trig functions, y = sinx, y = cosx and y = tanx. Chapter 7 Trigonometric Graphs Introduction We have alread looked at the graphs of various functions : The Linear function f() = The Quadratic function f() = The Hperbolic function f() = = = = We will

More information

Grade 7 & 8 Math Circles October 6, 2010 Graphs and Transformations

Grade 7 & 8 Math Circles October 6, 2010 Graphs and Transformations Universit of Waterloo Facult of Mathematics entre for Education in Mathematics and omputing Grade 7 & 8 Math ircles October, 00 Graphs and Transformations efinition Transformation: a transformation is

More information

Name Date Period. Worksheet 6.3 Volumes Show all work. No calculator unless stated. Multiple Choice

Name Date Period. Worksheet 6.3 Volumes Show all work. No calculator unless stated. Multiple Choice Name Date Period Worksheet 6. Volumes Show all work. No calculator unless stated. Multiple Choice. (Calculator Permitted) The base of a solid S is the region enclosed by the graph of y ln x, the line x

More information

3x 4y 2. 3y 4. Math 65 Weekly Activity 1 (50 points) Name: Simplify the following expressions. Make sure to use the = symbol appropriately.

3x 4y 2. 3y 4. Math 65 Weekly Activity 1 (50 points) Name: Simplify the following expressions. Make sure to use the = symbol appropriately. Math 65 Weekl Activit 1 (50 points) Name: Simplif the following epressions. Make sure to use the = smbol appropriatel. Due (1) (a) - 4 (b) ( - ) 4 () 8 + 5 6 () 1 5 5 Evaluate the epressions when = - and

More information

Three-Dimensional Coordinates

Three-Dimensional Coordinates CHAPTER Three-Dimensional Coordinates Three-dimensional movies superimpose two slightl different images, letting viewers with polaried eeglasses perceive depth (the third dimension) on a two-dimensional

More information

Grade 7/8 Math Circles Fall Nov.4/5 The Pythagorean Theorem

Grade 7/8 Math Circles Fall Nov.4/5 The Pythagorean Theorem 1 Faculty of Mathematics Waterloo, Ontario Centre for Education in Mathematics and Computing Grade 7/8 Math Circles Fall 2014 - Nov.4/5 The Pythagorean Theorem Introduction A right triangle is any triangle

More information

Chapter 13. Graphics, Animation, Sound and Drag-and-Drop The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill

Chapter 13. Graphics, Animation, Sound and Drag-and-Drop The McGraw-Hill Companies, Inc. All rights reserved. McGraw-Hill Chapter 13 Graphics, Animation, Sound and Drag-and-Drop McGraw-Hill 2010 The McGraw-Hill Companies, Inc. All rights reserved. Chapter Objectives - 1 Use Graphics methods to draw shapes, lines, and filled

More information

9. p(x) = x 3 8x 2 5x p(x) = x 3 + 3x 2 33x p(x) = x x p(x) = x 3 + 5x x p(x) = x 4 50x

9. p(x) = x 3 8x 2 5x p(x) = x 3 + 3x 2 33x p(x) = x x p(x) = x 3 + 5x x p(x) = x 4 50x Section 6.3 Etrema and Models 593 6.3 Eercises In Eercises 1-8, perform each of the following tasks for the given polnomial. i. Without the aid of a calculator, use an algebraic technique to identif the

More information

Isometry: When the preimage and image are congruent. It is a motion that preserves the size and shape of the image as it is transformed.

Isometry: When the preimage and image are congruent. It is a motion that preserves the size and shape of the image as it is transformed. Chapter Notes Notes #36: Translations and Smmetr (Sections.1,.) Transformation: A transformation of a geometric figure is a change in its position, shape or size. Preimage: The original figure. Image:

More information

UNIT 29 Using Graphs to Solve Equations: CSEC Revision Test

UNIT 29 Using Graphs to Solve Equations: CSEC Revision Test UNIT 9 Using Graphs to Solve : UNIT 9 Using Graphs to Solve 1. Shell bus 3 litres of oil and 40 litres of gasoline for $30. The cost of one litre of oil is $ and the cost of one litre of gasoline is $.

More information

Using a Table of Values to Sketch the Graph of a Polynomial Function

Using a Table of Values to Sketch the Graph of a Polynomial Function A point where the graph changes from decreasing to increasing is called a local minimum point. The -value of this point is less than those of neighbouring points. An inspection of the graphs of polnomial

More information