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

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

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

4. 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).

5. 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

6. 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.

7. 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

8. 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

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

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

11. 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)