Make your new weekly Warm up Page January 23-27, 2017 Monday Jan. 23 WRITE ON SHEET “warm up on daily notes” Do warm up on daily notes

Agenda: Warm up Week ahead…TEST FRIDAY Standard / I Can Lesson Exit ticket Problem set

Standard: 8.G.A.3 Describe the effect of dilations, translations, rotations, and reflections on a two dimensional figures using coordinates. I CAN…. describe what happens when two dimensional figures are dilated using coordinates.

Vocabulary dilation center of dilation scale factor

Your pupils are the black areas in the center of your eyes Your pupils are the black areas in the center of your eyes. When you go to the eye doctor, the doctor may dilate your pupils, which makes them larger. A dilation is a transformation that changes the size, but not the shape, of a figure.

Every dilation has a fixed point that is the center of dilation Every dilation has a fixed point that is the center of dilation. To find the center of dilation, draw a line that connects each pair of corresponding vertices. The lines intersect at one point. This point is the center of dilation.

Example 1 Tell whether each transformation is a dilation. Explain. Compare the ratios of corresponding side lengths. 2 6 1 3 BC B'C' = 2 6 1 3 AD A'D' = Yes; the ratios of corresponding side length are equal and corresponding angles are congruent.

Example 2 Tell whether each transformation is a dilation. Explain. Compare the ratios of corresponding side lengths. 4 2 BA B'A' = = 2 5 3 AC A'C' = 1.66 No; the ratios of corresponding side length are not equal.

The scale factor describes how much a figure is enlarged or reduced The scale factor describes how much a figure is enlarged or reduced. It represents the ratio of a length on the image to the corresponding lentth on the original figure.

Example 3 Dilate the figure below by a scale factor of 2. What are the vertices of the image? Multiply the coordinates by 2 to find the vertices of the image. A’B’C’ ABC A(2, 2) A’(2  2, 2  2) A’(4, 4) B(3, 4) B’(3  2, 4  2) B’(6, 8) C(5, 2) C’(5  2, 2  2) C’(10, 4) The vertices of the image are A’(4, 4), B’(6, 8), and C’(10, 4).

Example 4 Dilate the figure below by a scale factor of . What are the vertices of the image? 1 3 Multiply the coordinates by to find the vertices of the image. 1 3 A’B’C’ ABC A(3, 9) A’(3  , 9  ) A’(1, 3) 1 3 B(9, 6) B’(9  , 6  ) B’(3, 2) 1 3 C(6, 3) C’(6  , 3  ) C’(2, 1) 1 3 The vertices of the image are A’(1, 3), B’(3, 2), and C’(2, 1).

Example 5 Dilate the figure by a scale factor of 2. What are the vertices of the image? 2 4 6 8 10 C A B 2 4 6 8 10

A’B’C’ ABC A(2, 2) A’(2  2, 2  2) A’(4, 4) B(4, 2) B’(4  2, 2  2) B’(8, 4) C(2, 4) C’(2  2, 4  2) C’(4, 8) The vertices of the image are A’(4, 4), B’(8, 4), and C’(4, 8).

10 B’ C’ A’ 8 6 C 4 2 A B 2 4 6 8 10

Example 6 Dilate the figure by a scale factor of 0.5. What are the vertices of the image? 10 C 8 6 A B 4 2 2 4 6 8 10

A’B’C’ ABC A(4, 5) A’(4  0.5, 5  0.5) A’(2, 2.5) B(8, 5) B’(8  0.5, 5  0.5) B’(4, 2.5) C(4, 9) C’(4  0.5, 9  0.5) C’(2, 4.5) The vertices of the image are A’(2, 2.5), B’(4, 2.5), and C’(2, 4.5).

10 C 8 6 B’ C’ A’ A B 4 2 2 4 6 8 10

Exit Tiecket 3. Identify the transformation that is a dilation. A. A(0, 3), B(4, 4), C(2, 2)  A’(0, 9), B’(12, 12), C’(6, 6) B. A(2, 3), B(3, 5), C(5, 7)  A’(5, 6), B’(6, 8), C’(8, 10) C. A(5, 2), B(3, 7), C(7, 9)  A’(2, –1), B’(0, 4), C’(4, 6) D. A(1, 2), B(3, 4), C(5, 6)  A’(4, 5), B’(6, 7), C’(8, 9) Tell whether the transformation is a dilation. explain Explain.‏ 2. A triangle has vertices A'(2,4), B(5,6), and C(6,1). Dilate the figure by a scale factor of 2 with the origin as the center of dilation. What are the vertices of the image?

Student.demos.com Class code:RGQ65 http://www.hoodamath.com/mobile/games/transformationgolf.html 19 19