Dilations in the Coordinate Plane

What is a dilation?

• A better name is a projection.• The hands differ only in size, so dilations produce similar figures.• This dilation is an enlargement since the dilation

makes the image larger.• The original is called the pre-image and the

projection is called the image.• The “light source” of the projection is called the

center of the dilation

Dilations on the Coordinate Plane

• A dilation with its center at the origin (0,0) is obtained by multiplying the x and y coordinates of the pre-image points by the scale factor.• We use the variable “k” to represent the scale factor.• (x,y) -> (kx,ky) is the coordinate notation for a dilation centered at the

origin.• For us, k will be a positive number.• When k is greater than 1, the dilation is an enlargement.• When k is less than 1, the dilation is a reduction.

Example• Perform the specified

dilation and classify it as an enlargement or a reduction.

Since ½ is less than 1, we know it will be a reduction before we even begin.)

Pre-image Image

A(-2,4) A’(-1,2)

B(6,8) B’(3,4)

C(2,0) C’(1,0)

Complete Worksheet 6.6A for tomorrow.