Dilations in the Coordinate Plane

GeometryUnit 8, Day 7Ms. Reed

Dilations What is a dilation?

A transformation that changes the size of a figure.

What are two types of dilations? Enlargement Reduction

The point of projection is called the center of dilation

The amount of change is written as a ratio and is called a scale factor.

Dilations In the coordinate plane,

the center of dilation is the origin.

To find the new coordinates, multiply the original coordinates by the scale factor.

Steps to Follow1. Plot the given points.

2. Multiply each coordinate by the scale factor.

3. Plot the image points.

4. State the coordinates of the dilation.

Given the vertices of the triangle, find a dilation by a scale factor of 3.

A (1,2) B (3,3) C (1,3)

y

x

C B

A

C’B’

A’A’ (3,6)

B’ (9,9)

C’ (3,9)

Given the vertices of the rectangle, find a dilation by a scale factor of 2/3.

A (-6,-3) B (-6,3) C (6,3) D (6,-3)

y

x

A

B C

D

A’ (-4,-2)B’ (-4,2)

C’ (4,2)D’ (4,-2)

A’

B’ C’

D’

Practice with Dilations http://www.regentsprep.org/Regents/math/

geometry/GT3/PracCoD.htm

Homework

Work Packet: Dilations