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Coordinate Algebra 5.4

Coordinate Algebra 5.4. Geometric Stretching, Shrinking, and Dilations. Stretching/Shrinking. Horizontal. Vertical. Affects the y-values (x, 3y) is a vertical stretch (x, y) is a vertical shrink). Affects the x-values (2x, y) is a horizontal stretch ( x, y) is a horizontal shrink.

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Coordinate Algebra 5.4

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  1. Coordinate Algebra 5.4 Geometric Stretching, Shrinking, and Dilations

  2. Stretching/Shrinking Horizontal Vertical Affects the y-values (x, 3y) is a vertical stretch (x, y) is a vertical shrink) • Affects the x-values • (2x, y) is a horizontal stretch • (x, y) is a horizontal shrink

  3. Let’s Examine……..

  4. CAT C (-2, 0) A(1, -1) T(2, 3) T T’ C ‘(-6, 0) A’(3, -1) T’(6, 3) C C’ A A’

  5. Dilations

  6. What is a Dilation? • Dilation is a transformation that produces a figure similar to the original by proportionally shrinking or stretching the figure. Dilated PowerPoint Slide

  7. Adilationis a transformation that produces an image that is the same shapeas the original, but is a different size.

  8. What’s the difference? • A dilation occurs when you stretch or shrink both the x and y values by the same scale factor • Dilations preserve shape, whereas stretching and shrinking do not. • Dilations create similar figures • Angle measures stay the same • Side lengths are proportional

  9. Proportionally Let’s take a look… And, of course, increasing the circle increases the diameter. • When a figure is dilated, it must be proportionally larger or smaller than the original. So, we always have a circle with a certain diameter. We are just changing the size or scale. Decreasing the size of the circle decreases the diameter. We have a circle with a certain diameter. • Same shape, Different scale.

  10. Scale Factor and Center of Dilation When we describe dilations we use the terms scale factor and center of dilation. • Scale factor • Center of Dilation Here we have Igor. He is 3 feet tall and the greatest width across his body is 2 feet. He wishes he were 6 feet tall with a width of 4 feet. His center of dilation would be where the length and greatest width of his body intersect. He wishes he were larger by a scale factor of 2.

  11. Scale Factor • If the scale factor is larger than 1, the figure is enlarged. • If the scale factor is between 1 and 0, the figure is reduced in size. Scale factor > 1 0 < Scale Factor < 1

  12. Are the following enlarged or reduced?? C A Scale factor of 1.5 D Scale factor of 3 B Scale factor of 0.75 Scale factor of 1/5

  13. Example 1: • Quadrilateral ABCD has vertices A(-2, -1), B(-2, 1), C(2, 1) and D(1, -1). • Find the coordinates of the image for the dilation with a scale factor of 2 and center of dilation at the origin. • Multiply all values by 2! • A’(-4, -2) B’(-4, 2) C;(4, 2) and D’(2, -2) C’ B’ B C A D A’ D’

  14. F(-3, -3), O(3, 3), R(0, -3) Scale factor 1/3 Multiple all values by 1/3 (same as dividing by 3!) F’(-1, -1) O’(1, 1) R’(0, -1) Example 2: O O’ F’ R’ F R

  15. Finding a Scale Factor • The blue quadrilateral is a dilation image of the red quadrilateral. Describe the dilation. J(0, 2) J’(0, 1) K(6, 0) K’(3, 0) L(6, -4) L’(3, -2) M(-2,- 2) J’(-1, -1) All values have been divided by 2. This means there is a scale factor of ½. You have a reduction!

  16. Credits: • Gallatin Gateway School • Texas A&M • Your fabulous 9th grade math teachers!

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