Coordinate Algebra 5.4
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Transcript of Coordinate Algebra 5.4
Coordinate Algebra 5.4
Geometric Stretching, Shrinking, and Dilations
Stretching/ShrinkingHorizontal
• Affects the x-values• (2x, y) is a horizontal stretch• (x, y) is a horizontal shrink
Vertical• Affects the y-values• (x, 3y) is a vertical stretch• (x, y) is a vertical shrink)
Let’s Examine……..
CAT
C (-2, 0) A(1, -1) T(2, 3)
C ‘(-6, 0) A’(3, -1) T’(6, 3)
C’ A A’
T T’
C
Dilations
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
A dilation is a transformation that
produces an image that is the same shape as the original, but is a
different size.
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
• When 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.
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.
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.
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??
AC
DB
Scale factor of 0.75
Scale factor of 3
Scale factor of 1/5
Scale factor of 1.5
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)
A
B C
A’
B’ C’
D
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)
F
O
R
F’
O’
R’
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!
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Credits:
• Gallatin Gateway School• Texas A&M• Your fabulous 9th grade math teachers!