Geometric Stretching Shrinking and Dilations StretchingShrinking Horizontal Affects the xvalues 2x y is a horizontal stretch x y is a horizontal shrink Vertical Affects the yvalues ID: 1044911
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1. Coordinate Algebra 16.5Geometric Stretching, Shrinking, and Dilations
2. Stretching/ShrinkingHorizontalAffects the x-values(2x, y) is a horizontal stretch(x, y) is a horizontal shrink VerticalAffects the y-values(x, 3y) is a vertical stretch(x, y) is a vertical shrink)
3. Let’s Examine……..
4. CAT C (-2, 0) A(1, -1) T(2, 3)C ‘(-6, 0) A’(3, -1) T’(6, 3)C’AA’TT’C
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. A dilation is a transformation that produces an image that is the same shape as 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 factorDilations preserve shape, whereas stretching and shrinking do not. Dilations create similar figures Angle measures stay the sameSide lengths are proportional
9. ProportionallyWhen a figure is dilated, it must be proportionally larger or smaller than the original.Same shape, Different scale.Let’s take a look…We have a circle with a certain diameter.Decreasing the size of the circle decreases the diameter.And, of course, increasing the circle increases the diameter. So, we always have a circle with a certain diameter. We are just changing the size or scale.
10. Scale Factor and Center of DilationWhen we describe dilations we use the terms scale factor and center of dilation.Scale factor Center of DilationHere 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.He wishes he were larger by a scale factor of 2.His center of dilation would be where the length and greatest width of his body intersect.
11. Scale FactorIf 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 > 10 < Scale Factor < 1
12. Are the following enlarged or reduced??ACDBScale factor of 0.75Scale factor of 3Scale factor of 1/5Scale 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)ABCA’B’C’DD’
14. Example 2: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)FORF’O’R’
15. Finding a Scale FactorThe 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 SchoolTexas A&MYour fabulous 9th grade math teachers!