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Coordinate Algebra 5.4

Explore the concepts of geometric transformations, focusing on stretching, shrinking, and dilations. Learn how these transformations affect the x and y coordinates of figures, and understand the distinction between simple transformations and dilations. This engaging presentation covers the definition of dilations, the importance of scale factors and centers of dilation, and provides examples to illustrate these concepts in practice. Perfect for 9th-grade math students, this resource makes geometry both accessible and exciting!

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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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