Example 1

Use the coordinate mapping (x, y) → (x + 8, y + 3) to translate ΔSAM to create ΔS’A’M’.

6.7: Similarity Transformations

Objectives:

1. To use dilations to create similar figures

2. To perform dilations in the coordinate plane using coordinate notation

Dilations

A dilation is a type of transformation that enlarges or reduces a figure.

The dilation is described by a scale factor and a center of dilation.

The scale factor k is the ratio of the length of any side in the image to the length of its corresponding side in the preimage.

Dilations

Orig

Ne

in

w Si

al

d

de

e

Sik

Example 2

What happens to any point (x, y) under a dilation centered at the origin with a scale factor of k?

Dilations in the Coordinate PlaneYou can describe a

dilation with respect to the origin with the notation (x, y) → (kx, ky), where k is the scale factor.

Dilations in the Coordinate PlaneYou can describe a

dilation with respect to the origin with the notation (x, y) → (kx, ky), where k is the scale factor.

Enlargement: k > 1.

Dilations in the Coordinate PlaneYou can describe a

dilation with respect to the origin with the notation (x, y) → (kx, ky), where k is the scale factor.

Reduction: 0 < k < 1.

Example 3

Determine if ABCD and A’B’C’D’ are similar figures. If so, identify the scale factor of the dilation that maps ABCD onto A’B’C’D’ as well as the center of dilation.

Is this a reduction or an enlargement?

Yes. s.f.=1/3. reduction

Example 4

A graph shows PQR with vertices P(2, 4), Q(8, 6), and R(6, 2), and segment ST with endpoints S(5, 10) and T(15, 5). At what coordinate would vertex U be placed to create ΔSUT, a triangle similar to ΔPQR?

Do this on graph paper and tape/glue into your notebook

Example 5

Figure J’K’L’M’N’ is a dilation of figure JKLMN. Find the coordinates of J’ and M’.

(-1,-2)