Dilations on the Coordinate Plane

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Presentation transcript:

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 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 sides four times the size of triangle ABC

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)

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

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 x3 x3 x3 x3 x3 x3 x3 M’(-6 , 6) A’(6 , 6) T’(6 , -6) H’(-6 , -6)

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

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

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!

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!

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

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!!!