Dilations 8.7 2016.notebook
DILATIONS - a transformation that results in an image that
is the _____________ as the original, but is
_______________.
The image after a dilation is _____________ to the pre-image.
Scale Factor =
Enlargement: If the scale factor is greater than 1 (the image is larger)
Reduction: If the scale factor is between 0 and 1 (the image is smaller)
Dilations affect all sides of a figure, but
Angle measures remain the same
Is a Dilation an isometry?
Transformation rule: (x,y) --> (kx,ky),
when center of dilation is (0,0)
Example 1: If the scale factor is 3, how would you write the rule?
Dilate the point (-2, 9) by a scale factor of 1/3.
Example 2: Triangle ABC has vertices A (0, 2), B (4, 4), and
What are the vertices of its image with a scale factor of 4?
C (-1, 4).
Dilations 8.7 2016.notebook
Scale factor = CP' CP
Dilations in the coordinate plane centered at the origin follow the rule: (x,y) ­­> (kx, ky), where k is the scale factor.
An example of a dilation with a scale factor of 2:
Is triangle XYZ similar to triangle X'Y'Z' ?
Find the lengths of :
XY and X'Y'
XZ and X'Z'
Dilations 8.7 2016.notebook
Example 3: Coordinate Plane
Quadrilateral PQRS has vertices P (-2, 4), Q (4, 4), R (4, -2), and
S (- 4, - 4). It is dilated by a scale factor of ½.
Verify the quads are similar by comparing their side
lengths.
Find the vertices of the image under this dilation.
Dilations 8.7 2016.notebook
Example 5:
Quadrilateral A‛B‛C‛D‛ is a dilation of quadrilateral ABCD.
Find the scale factor. Classify the dilation as an enlargement or a reduction
What are the lengths from the origin to A and A'?
What are the lengths of AB and A'B'?
Dilations 8.7 2016.notebook
Summary: Dilations around a center that is the origin...
A'=
B'=
A, A' and the center of dilation will always be collinear!
Dilations around a center that is NOT the origin...
For a scale factor that is less than 1, we can do the same thing...
for k = 1/2, divide the rise and run in half Notice that the pre­image, image and center are still all collinear!!
Dilations 8.7 2016.notebook