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 5 E 7 1 and F 1 5 ID: 1044909
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2. Warm UpSimplify 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)5. E(–7, –1) and F(–1, –5)
3. Apply similarity properties in the coordinate plane.Use coordinate proof to prove figures similar.Objectives
4. dilationscale factorVocabulary
5. A dilation is a transformation that changes the size of a figure but not its shape. The preimage and the image are always similar.
6. Scale Factor – the ratio of image to its pre-imageThe ratio of corresponding sides
7. Scale FactorWhen scale factor is greater than 1, the shape gets bigger (enlargement).When scale factor is less than 1, but greater than 0, the shape gets smaller (reduction).
8. SCALE FACTOR.2657314610BDAC
9. Find the coordinates of the dilation image for the given scale factor, k.Example 1:G(0, -2), H(1, 3), and I(4, 1); k = 2All you do is multiply k to (x, y).G’( , ), H’( , ), and I’( , )
10. Find the coordinates of the dilation image for the given scale factor, k.Example 2:L(8, -8), N(0, 16), and M(4, 5); k = 1/4All you do is multiply k to (x, y).L’( , ), N’( , ), and M’( , )
11. k = 1/2
12. k = 2
13. Example 1: Computer Graphics ApplicationDraw the border of the photo after a dilation with scale factor
14. Example 1 ContinuedRectangleABCD Step 1 Multiply the vertices of the photo A(0, 0), B(0, 4), C(3, 4), and D(3, 0) by RectangleA’B’C’D’
15. Example 1 ContinuedStep 2 Plot points A’(0, 0), B’(0, 10), C’(7.5, 10), and D’(7.5, 0).Draw the rectangle.
16. Example 2: Finding Coordinates of Similar TriangleGiven 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.12OU = 144Cross Products Prop.OU = 12Divide both sides by 12.
17. Example 2 ContinuedU lies on the y-axis, so its x-coordinate is 0. Since OU = 12, its y-coordinate must be 12. The coordinates of U are (0, 12).So the scale factor is
18. Check It Out! Example 2 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, Substitute 10 for OM, 15 for OP, and 30 for OQ.15 ON = 300Cross Products Prop.ON = 20Divide both sides by 15.
19. Check It Out! Example 2 ContinuedN lies on the y-axis, so its x-coordinate is 0. Since ON = 20, its y-coordinate must be –20. The coordinates of N are (0, –20).So the scale factor is
20. Lesson Quiz: Part I1. 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)
21. Lesson Quiz: Part II3. Given: A(–1, 0), B(–4, 5), C(2, 2), D(2, –1), E(–4, 9), and F(8, 3) Prove: ∆ABC ~ ∆DEF Therefore, and ∆ABC ~ ∆DEFby SSS ~.