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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

Coordinate Algebra 5.4

Geometric Stretching, Shrinking, and Dilations

stretching shrinking
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
slide4
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’

what is a dilation
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

slide7

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

what s the difference
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
proportionally
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.
scale factor and center of dilation
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.

scale factor
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

are the following enlarged or reduced
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

example 1
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’

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)

Example 2:

O

O’

F’

R’

F

R

finding a scale factor
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!

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