Geometric Transformations

Dilations & Reductions

Definitions

• Dilation: transformation that produces an image that is the same shape as the original, but a different size

• Enlargement: image bigger than the preimage• Reduction: image smaller than the preimage• Scale factor: how much the preimage changes• Center of dilation: self explanatory—the

center of the preimage/image

Example

Draw the dilation of ∆ABC with vertices A(-1,-1), B(0,2), C(1,-2), with the center of dilation at the origin and a scale factor of 3.

Example

Draw the dilation of ∆EFG with vertices E(0,0), F(0,6), G(8,0), center of dilation at E, and scale factor of ½ .

Example

Draw ABCD: A(1,1), B(5,1), C(1,5), D(5,5)

Dilate by a scale factor of ½.Translate 3 up, 4 left.Reflect over the y-axis.

Example

Draw JKLM: J(2,-2), K(1,1), L(-2,-3), M(0,-5)

Reflect over the y-axis.

Rotate 180 degrees around the origin.