Dilations and Similarity in the Coordinate Plane 7-6 Warm Up Lesson Presentation Lesson Quiz Holt Geometry

Warm Up Simplify each radical. 1. 2. 3. Find the distance between each pair of points. Write your answer in simplest radical form. 4. C (1, 6) and D (–2, 0)

Learning Targets Apply similarity properties in the coordinate plane. Use coordinate proof to prove figures similar.

You know this already!! A dilation is a transformation that changes the size of a figure but not its shape. The preimage and the image are always similar. A scale factor describes how much the figure is enlarged or reduced. For a dilation with scale factor k, you can find the image of a point by multiplying each coordinate by k: (x, y)  (kx, ky).

If the scale factor of a dilation is greater than 1 (k > 1), it is an enlargement. If the scale factor is less than 1 (k < 1), it is a reduction. Helpful Hint

Example 2: Finding Coordinates of Similar Triangle Given that ∆TUO ~ ∆RSO, find the coordinates of U and the scale factor. Since ∆TUO ~ ∆RSO, Substitute 12 for RO, 9 for TO, and 16 for OY. ----- Meeting Notes (3/11/14 10:37) ----- start here tomorrow period 3! U(0,12) 12OU = 144 Cross Products Prop. OU = 12 Divide both sides by 12.

Check It Out! Example 3 Given that ∆MON ~ ∆POQ and coordinates P (–15, 0), M(–10, 0), and Q(0, –30), find the coordinates of N and the scale factor. Since ∆MON ~ ∆POQ, 15 ON = 300 N(0,-20) ON = 20

Example 4: Proving Triangles Are Similar Given: E(–2, –6), F(–3, –2), G(2, –2), H(–4, 2), and J(6, 2). Prove: ∆EHJ ~ ∆EFG. Step 1 Plot the points and draw the triangles. Left off here period 5

Example 4 Continued Step 2 Use the Distance Formula to find the side lengths.

Example 4 Continued Step 3 Find the similarity ratio. = 2 = 2 Since and E  E, by the Reflexive Property, ∆EHJ ~ ∆EFG by SAS ~ .

Lesson Quiz: Part I 1. Given X(0, 2), Y(–2, 2), and Z(–2, 0), find the coordinates of X', Y, and Z' after a dilation with scale factor –4. 2. ∆JOK ~ ∆LOM. Find the coordinates of M and the scale factor. X'(0, –8); Y'(8, –8); Z'(8, 0)