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

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1 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 now on we will refer to the dots on a graph as points. Vocabular -coordinate -coordinate point of origin The point on the graph is described this wa: point = (, ) The coordinates for a point (, ) are made up of two parts. The first part is the -coordinate, and the second part is the -coordinate. In the graph, Point has the coordinates (, ). Eample Locate (, ) on the coordinate graph. = (, ) Go right on the -ais to and then up the -ais to. Unit Lesson 9

2 Lesson Coordinate graphs are divided into four sections, or quadrants. We use Roman numerals to label these quadrants. II III I IV Now let s put points in each section, or quadrant, of the graph. Point -coordinate -coordinate Quadrant How We Write It I = (, ) II = (, ) C III C = (, ) D IV D = (, ) 9 Unit Lesson

3 Lesson, II (, ) (, ) C III, (, ), I IV (, ), D Notice there are - and -coordinates in each corner of the graph to help us see a pattern. For points in Quadrant I, like Point, the coordinates are both positive. For points in Quadrant II, like Point, the -coordinate is alwas negative and the -coordinate is positive. ll the coordinates in Quadrant III for Point C are negative. For points in Quadrant IV, like Point D, the -coordinate is alwas positive and the -coordinate is negative. The place where the - and -aes cross is (0, 0). This point is called the point of origin. Unit Lesson 9

4 Lesson What shape is it? One of the important uses of the coordinate graph is to help us understand geometr. We can learn a lot about different shapes b seeing them on a coordinate graph. For one thing, it gives us a wa to assign numbers to the different vertices. Remember, the vertices of a shape are the points where the sides meet. We can use the coordinates of the vertices to tell us more about the properties of the shape. Here is an eample of a square on a coordinate graph. Notice the coordinates of the vertices. Eample What are the coordinates of the vertices of square CD? C D 9 Unit Lesson

5 Lesson The coordinates are: (, ), (, ), C (, ), and D (, ). (, ) (, ) C D (, ) (, ) The coordinate graph gives us more was to describe the shape. We could discuss its location (in Quadrant I). We could talk about the signs of the coordinates of the vertices (all are positive). We could compare the different numbers in the coordinates (the are all s and s, in different orders and combinations). There are man new things to look at when we put the shape on a graph. Sometimes, we can even predict what the shape is if we are given its coordinates without its picture. Let s see if we can guess what shape is represented in the net eample. Unit Lesson 99

6 Lesson Eample Identif the shape with these vertices. Use a graph to check our answer. (, ) (, ) C (, ) There are onl three sets of coordinates. That means it is a triangle. C The three vertices are the clue that told us there are three sides. Triangles are shapes with three sides. s we get better at recognizing shapes b their coordinates, we would also notice that it is an equilateral triangle. This can be determined b looking at the coordinates and the distances between them. We will work more with coordinates and shapes in later lessons, where we will learn some of the important patterns. 00 Unit Lesson Problem-Solving ctivit Turn to Interactive Tet, page 0. Reinforce Understanding Use the mook Stud Guide to review lesson concepts.

7 Lesson Homework ctivit Write > or < to show which is the larger number ctivit Solve the addition and subtraction problems with positive and negative numbers. For the subtraction problems, remember to add the opposite ctivit Tell which quadrant ou would find each point in on a coordinate graph. nswer I, II, III, or IV.. (, ). (, ). (, ). (, ). (, ). (, ). (, ). (, ) ctivit Distributed Practice Solve.. Convert % to a fraction.. Convert 0. to a percent. 00. Convert to a decimal number II III I IV Copright 00 b Cambium Learning Sopris West. ll rights reserved. Permission is granted to reproduce this page for student use. Unit Lesson 0