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Dilations on the Coordinate Plane

Dilations on the Coordinate Plane. Dilations on the Coordinate Plane. Enlarging or reducing a figure is called a dilation A dilated figure is similar to the original figure The ratio of the new figure to the original is called a scale factor. Dilations on the Coordinate Plane.

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Dilations on the Coordinate Plane

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  1. Dilations on the Coordinate Plane

  2. Dilations on the Coordinate Plane • Enlarging or reducing a figure is called a dilation • A dilated figure is similar to the original figure • The ratio of the new figure to the original is called a scale factor

  3. Dilations on the Coordinate Plane • If triangle ABC is dilated by scale factor of 2, triangle A’B’C’ will have sides twice as big as triangle ABC • If triangle ABC is dilated by scale factor of 4, triangle A’B’C’ will have sidesfour times the size of triangle ABC

  4. Dilation Mini-Lab In this lab you will… • Graph square MATH with vertices at M(-2, 2), A(2, 2), T(2, -2) and H(-2, -2) • Then dilate the figure by a scale factor of 3 • To find the vertices of the dilation, multiply each coordinate in the ordered pairs by the scale factor (3)

  5. Dilation Mini-Lab • Graph square MATH with vertices at M(-2, 2), A(2, 2), T(2, -2) and H(-2, -2) M A H T

  6. Dilation Mini-Lab • To find the vertices of the dilation, multiply each coordinate in the ordered pairs by the scale factor (3) M (-2 , 2) A (2 , 2) T (2 , -2) H (-2 , -2) x3 x3x3 x3x3 x3x3x3 M’(-6 , 6) A’(6 , 6) T’(6 , -6) H’(-6 , -6)

  7. Dilation Mini-Lab • Graph square M’A’T’H’ with vertices at M’(-6, 6), A’(6, 6), T’(6, -6) and H’(-6, -6) M’ A’ H’ T’ M A H T

  8. Dilation Mini-Lab • To check your graph, draw lines through the origin and each of the vertices of the original figure • If the vertices of the dilated figure don’t lie on the same lines you’ve made a mistake M’ A’ H’ T’ M A H T

  9. Dilation Mini-Lab • What do you think happens if you dilate a figure to a scale factor of 1? • Multiply each coordinate in triangle ABC with vertices A(2, 12), B(12, 4), and C(20, 20) by a scale factor of 1 • What do you notice? The coordinates stay the same!

  10. Dilation Mini-Lab • What do you think happens if you dilate a figure to a scale factor of ½ ? • On graph paper, graph triangle ABC with vertices A(2, 12), B(12, 4), and C(20, 20) • Multiply each coordinate in triangle ABC by a scale factor of ½ • Graph triangle A’B’C’ • What do you notice? Triangle A’B’C’ has sides half the size of triangle ABC!

  11. Dilation Checkpoint • What are the coordinates of Point A’ if Point A (3, 7) were dilated to a scale factor of 4? • What are the coordinates of Point A’ if Point A (3, 7) were dilated to a scale factor of 10? • What is the length of line segment A’B’ if an 8” line segment AB were dilated to a scale factor of 3? A’ (12, 28) A’ (30, 70) 24 Inches

  12. Homework • Practice Worksheet 9-8 (both sides) • Due Tomorrow! • Review is scheduled for Tomorrow and the Coordinate Plane Test is scheduled for FRIDAY!. • Study for the test!!!

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