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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Geometric Stretching, Shrinking, and Dilations
Affects the y-values
(x, 3y) is a vertical stretch
(x, y) is a vertical shrink)
C (-2, 0) A(1, -1) T(2, 3)
C ‘(-6, 0) A’(3, -1) T’(6, 3)
Dilated PowerPoint Slide
Adilationis a transformation that produces an image that is the same shapeas the original, but is a different size.
Let’s take a look…
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.
Decreasing the size of the circle decreases the diameter.
We have a circle with a certain diameter.
When we describe dilations we use the terms scale factor and 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.
Scale factor > 1
0 < Scale Factor < 1
Scale factor of 1.5
Scale factor of 3
Scale factor of 0.75
Scale factor of 1/5
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!