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Dilations
Vocabulary
Dilation: The image created by enlarging or
reducing a figure.
 Center: The center of a dilation is a fixed
point used for measurement when altering
the size of the figure.
 Enlargement: An image that is larger than
the original figure. An enlargement has a
scale factor greater than 1.
 Reduction: An image that is smaller than the
original figure. A reduction has a scale factor
between 0 and 1


A dilation is ALWAYS similar to the original
figure. So the corresponding angles are
congruent and corresponding sides are
proportional.

Scale Factor: The ratio of a length on the
image to a length on the original figure is
the scale factor of the dilation.
Examples
Graph
JKL with vertices
J (3,8), K (10,6), and L (8,2). Then graph its
image J’K’L’ after a dilation with a scale factor
of ½.
Find the coordinates of the image of triangle
JKL after a dilation with each scale factor.
Then graph JKL and J’K’L’.
 A) Scale Factor 3
 B) Scale Factor 1/3

Find and Classify a Scale Factor

Quadrilateral V’Z’X’W’ is a dilation of
quadrilateral VZXW. Find the scale factor of
the dilation, and classify it as an enlargement
or a reduction.
Graph V’Z’X’W’
V’ (-5, 5)
Z’ (-2.5, 7.5)
X’ (2.5, 6)
W’ (5, 2.5)
Graph VZXW
V (-2,2)
Z (-1, 3)
X (1, 2.5)
W (2, 1)

Write a ratio of the x-or the y-coordinate of
one vertex of the DILATION to the x- or ycoordinate of the CORRESPONDING vertex of
the original figure.
Let’s use V and V’ since we have whole
numbers.
 V (-2, 2)
 V’ (-5, 5)

Y-coordinate of V’ = 5
Y-coordinate of V
2

Our scale factor is 5/2

Based on our scale factor our image is an
enlargement since 5/2 is greater than 1.

Remember 5/2 is an improper fraction so if
we change this into a mixed number we get
2.5
Carleta’s optometrist dilates her pupils by a
factor of 5/3. if her pupil before dilation has
a diameter of 5 milimeters, find the new
diameter after her pupil is dilated