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BELL RINGER

BELL RINGER. Graph  ABC with vertices A (0, 6), B (-2, 3), and C (2, 1). Then find the coordinates of its vertices if it is translated by (-4, -3). Graph the translation image. BELL RINGER - ANS.

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BELL RINGER

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  1. BELL RINGER Graph ABC with vertices A(0, 6), B(-2, 3), and C(2, 1). Then find the coordinates of its vertices if it is translated by (-4, -3). Graph the translation image.

  2. BELL RINGER - ANS To find the coordinates of the vertices of A’B’C’, add -4 to each x-coordinate and add -3 to each y-coordinate of ABC: (x - 4, y - 3). A(0, 6) + (-4, -3)  A(0 + (-4), 6 + (-3)) or A(-4, 3) B(-2, 3) + (-4, -3)  B(-2 + (-4), 3 + (-3)) or B(-6, 0) C(2, 1) + (-4, -3)  C(2 + (-4), 1 + (-3)) or C(-2, -2) The coordinates of the vertices of A’B’C’ are A(-4, 3), B(-6, 0),and C(-2, -2).

  3. DILATIONS Ms. Charlestin 9-4-13 HW: Pg. 705-707 #12-26 all

  4. Standards Objective: You will learn to investigate and draw dilations on a coordinate plane • MCC9-12.G.SRT.1 Verify experimentally the properties of dilations given by a center and a scale factor: a. A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged. b. The dilation of a line segment is longer or shorter in the ratio given by the scale factor.

  5. Dilations: (Stretching/Shrinking) • Dilations use a scale factor to reduce or enlarge shapes. • Every dilation has a center and a scale factor. Most of the time it is the origin (0, 0) • Scale Factor: tells you how many times larger or smaller your image will be. • The new shape and the image are similar. Dilations are also called similarity transformations.

  6. Finding a Dilation To find a dilation with center C and scale factor n, you can use the following two rules. • The image C is itself (meaning C’=C) • For any point R, R’ is on CR and CR’ = n•CR.

  7. How do we locate dilation images? • A dilation is a transformation who preimage and image are similar. A dilation is not an isometry. • Every dilation has a center and a scale factor n, n >0. The scale factor describes the size change from the original figure to the image.

  8. Example 1: • Quadrilateral ABCD has vertices A(-2, -1), B(-2, 1), C(2, 1) and D(1, -1). • Find the coordinates of the image for the dilation with a scale factor of 2 and center of dilation at the origin. C’ B’ B C A D A’ D’

  9. F(-3, -3), O(3, 3), R(0, -3) Scale factor 1/3 Example 2: O O’ F’ R’ F R

  10. T(-1, 0), H(1, 0), I(2, -2), S(-2, -2) Scale factor 4 Example 3: T H H’ T’ S I I’ S’

  11. The dilation is an enlargement if the scale factor is > 1. The dilation is a reduction if the scale factor is between 0 and 1.

  12. Finding a Scale Factor • The blue triangle is a dilation image of the red triangle. Describe the dilation. • The center is X. The image is larger than the preimage, so the dilation is an enlargement.

  13. Finding a Scale Factor • The blue quadrilateral is a dilation image of the red quadrilateral. Describe the dilation.

  14. Graphing Dilation Images • ∆PZG has vertices P(2,0), Z(-1, ½), and G (1, -2). What are the coordinates of the image of P for a dilation with center (0,0) and scale factor 3? a) (5, 3) b) (6,0) c) (2/3, 0) d) (3, -6)

  15. Solution: The scale factor is 3, so use the rule: (x, y)(3x, 3y). P(2,0) P’(3•2, 3•0) or P’(6, 0). The correct answer is B. What are the coordinates for G’ and Z’? Graphing Dilation Images

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