6th Grade Math Textbook, Fundamentals

 &KDSWHU

13-12

Graph Dilations

Objective To identify graphs of dilations of figures • To graph dilations of polygons on the

coordinate plane • To compute length and area on the coordinate plane

To advertise an art show, Beth uses a triangle. She dilates the triangle

to be three times as large so she can print it on posters. She dilates the

pattern to be half as large so she can print it on postcards. What are

the coordinates of the enlargement and the reduction images?

A is a transformation that reduces or enlarges the size

of a figure. A dilation does not change the shape of a figure;

its image is similar to the original figure. An is a

dilation that is larger than the original figure. A is

a dilation that is smaller than the original figure.

To dilate a polygon on a coordinate plane, multiply the x- and

y-coordinates of each vertex by the same positive number, the

scale factor. Then connect the vertices to form the image.

To find the coordinates of both images, dilate the triangle

according to the scale factor.

reduction

enlargement

dilation^0

y

x

  



















Y Z

X

Remember:Scale factor is the

ratio of the lengths of two

corresponding sides of two similar

polygons.

Enlargement

Multiply both coordinates of each vertex

by the scale factor of 3. Graph the images

of each vertex and connect them to form

the image.

P(x, y) P′(3x, 3y)

X(0, 4) X′(3 • 0, 3 • 4) X′(0, 12)

Y(3, 0) Y′(3 • (3), 3 • 0) Y′(9, 0)

Z(3, 0) Z′(3 • 3, 3 • 0) Z′(9, 0)

0

y

x

  



























Y‘ Z Z‘

X

Y

X‘

Reduction

Multiply both coordinates of each vertex by

the scale factor of. Graph the images of each

vertex and connect them to form the image.

P(x, y) P′( , )

X(0, 4) X′(0 • , 4 • ) X′(0, 2)

Y(3, 0) Y′(3 • , 0 • ) Y′(1.5, 0)

Z(3, 0) Z′(3 • , 0 • ) Z′(1.5, 0)

y

2

x

2

1

2

1

2

1

2

1

2

1

2

1

2

0

y

x

  



















Y Z

X

X‘

Y‘ Z‘

1

2

If the scale factor is between 0 and 1, the dilation is a reduction.

If the scale factor is greater than 1, the dilation is an enlargement.