By: Caroline, Jenny, Jennifer, Jared, Kaleigh

Transcription

1 By: Caroline, Jenny, Jennifer, Jared, Kaleigh

2 1) What are the coordinates of the image of (2, 5) after a counterclockwise rotation of 90º about the origin? 1) ( 2, 5) 2) (2, 5) 3) ( 5, 2) 4) (5, 2)

3 A dilation is a used to create an image that is larger or smaller than the original. If the new image is larger, it is called an enlargement. If the new image is smaller than the original, it is a reduction. Also, the original figure and its dilation are always similar figures.

4 The scale factor of a dilation determines its size. If the scale factor is greater than one, the dilation is an enlargement. If the scale factor is less than one, the dilation will be a reduction. Reduction- a dilation with 0 < k < 1 Enlargement- a dilation with k > 1 K represents the scale factor D k (x, y) = (kx, ky)

5 During dilations, there are some properties that remain the same throughout. 1. Angle measures 2. Parallelism (line that are parallel remain parallel) 3. Colinearity (points remain on the same line) 4. Midpoints 5. Orientation (order of the letters) However, one thing that DOES change during dilations, is isometry. A line segment will not stay the same length in all cases, unless the scale factor is one.

6 On the accompanying grid, graph and label quadrilateral ABCD, whose coordinates are A(-1,3) B(2,0) C2,-1) and D(-3,-1). Graph, label, and state the coordinates of A`B`C`D`, the image of ABCD under a dilation of 2, where the center of dilation is the origin. C(2,-1) 2x2=4-1x2=-2 C`=(4,-2) A` A A (-1,3) -1x2=-2 3x2=6 A`=(-2,6) D(-3,-1) -3x2=-6-1x2=-2 D`=(-6,-2) D` D B C B` C` B(2,0) 2x2=4 0x2=0 B`=(4,0)

7 What are the coordinates of the point (1,5) after being dilated by (-2,-10) Find the dilation image of the point (-8,12) after being dilated by D⅟₂ (-4,6) In which quadrant would the image of point (1,-2) fall after a dilation using a factor of -3? A) I B) II C) III D) IV When a dilation is performed on a hexagon, which property of the hexagon will not be preserved in its image? (1) parallelism (3) length of sides (2) orientation (4) measure of angles

8 Using a drawing program, a computer graphics designer constructs a circle on a coordinate plane on her computer screen. She determines that the equation of the circle s graph is (x-3)²+(y+2) ²=36. She then dilates the circle with the dilation After this transformation, what is the center of the new circle? A. (6,-5) B. (-6,5) C. (9,-6) D. (-9,6)

9 There are two different types of symmetry: line symmetry and rotational symmetry. Line symmetry, or reflection symmetry, is if the figure can be reflected onto itself by a line. Rotational symmetry, or radial symmetry is if the figure can be mapped onto itself by a rotation that is greater than 0 and less than 360. The number of times a figure can map onto itself is the order of symmetry. The magnitude of symmetry is the smallest angle that a figure can rotate to map onto itself. To calculate the magnitude of symmetry: m = 360 n (n is number of sides)

10 Line Symmetry Each figure has line symmetry because they can be mapped onto themselves over a single line. Rotational Symmetry

11 State whether the following figure has reflectional symmetry, rotational symmetry, both kinds of symmetry, or neither kind of symmetry. Vertical, horizontal, and diagonal reflectional symmetry, and rotational symmetry Vertical reflectional symmetry

12 A line of symmetry for the figure is shown. Find the coordinates of point A. +4 (5,2) +4 A`

13 A) H B) O C) A D) O E) E F) G

14 Line Symmetry (Reflection Symmetry)- divides the figure into two congruent halves. Angle of Rotational Symmetry- The smallest angle through which the figure is rotated to coincide with itself. Order of Rotational Symmetry- the number of times that you can get an identical figure when repeating the degree of rotation. Order of Symmetry- number of times a figure maps onto itself as it rotates from 0º to 360º

15 Dilation-creates an image that is larger or smaller than the original. Smaller image-reduction has occurred with a dilation with 0 < k< 1 Larger image-enlargement is a dilation with k >1 > Scale Factor-determine its size K represents the scale factor D k (x,y) = (kx,ky) Properties preserved under dilation: 1. Angle measures (remain the same) 2. Colinearity (points stay on the same lines) 3. Midpoint (midpoints remain the same in each) 4. Parallelism (parallel lines remain parallel) 5. Orientation (lettering order remains the same) 6. Distance is NOT preserved (lengths of segments are NOT the same in all cases except scale factor or 1.)

16 The rectangular prism shown is enlarged by dilation with scale factor 4. Find the surface area and volume of the image. SA= 2LH + 2HW + 2LW SA= 2(20)(12)+2(12)(8)+2(20)(8) SA= SA= 992 cm 3 12 V= L*W*H V= 12*20*8 V = 1920 cm3 20 8

17 1) The image of (-2,6) after a dilation with respect to the origin is (- 10,30). What is the constant of the dilation? [1] 5 [2] 8 [3] 10 [4] -8 2) Which special quadrilaterals have both rotational and line symmetry? [1] Rhombus [2] Square [3] Rectangle [4] All of above 3) The image of point A after a dilation of 3 is (6, 15). What was the original location of point A? [1] (2, 5) [2] (3, 12) [3] (9, 18) [4] (18, 45)