Notes 49 Dilations

A dilation is a transformation that changes the size, but not the shape, of a figure. After a dilation, the image of a figure is similar to the preimage.

Additional Example 1A: Identifying Dilations Tell whether each transformation is a dilation. The figures are not similar, so the transformation is not a dilation.

Additional Example 1B: Identifying Dilations Tell whether each transformation is a dilation. The figures are similar, so the transformation Is a dilation.

Tell whether each transformation is a dilation. Check It Out: Example 1A Tell whether each transformation is a dilation. A B A’ B’ 3 cm 6 cm C’ D’ 5 cm D C 10 cm

Tell whether each transformation is a dilation. Check It Out: Example 1B Tell whether each transformation is a dilation. Y X’ 13 yd 6 yd 6 yd 5 yd X z z’ 6 yd Y’ 12 yd

Similar figures have the same shape but not necessarily the same size. Remember!

Additional Example 2: Using Dilation to Enlarge a Figure Draw the vertices of the image of ∆ABC after a dilation by a scale factor of 2. What are the vertices of the image? Write the coordinates of the vertices of ABC. Then multiply the coordinates by 2 to find the coordinates of the vertices of A'B'C'.

Additional Example 2 Continued A’B’C’ ABC A(0, 0) A’(0  2, 0  2) A’(0, 0) B(1, 2) B’(1  2, 2  2) B’(2, 4) C(3, 1) C’(3  2, 1  2) C’(6, 2) The vertices of the image are A’(0, 0), B’(2, 4), and C’(6, 2).

Additional Example 2 Continued

Check It Out: Example 2A Find the vertices of the image of each figure after a dilation by the given scale factor. Then draw the image. Scale factor 3

Check It Out: Example 2B Find the vertices of the image of each figure after a dilation by the given scale factor. Then draw the image. Scale factor 2

Additional Example 3: Using a Dilation to Reduce a Figure Draw the image of ∆DEF after a dilation by a scale factor of . Then draw the image. 1 3 Write the coordinates of the vertices of DEF. The multiply the coordinates by 1/3 to find the coordinates of the vertices of D‘E‘F'. D’E’F’ DEF D(3, 3) D’(3  , 3  ) D’(1, 1) 1 3 E(6, 6) E’(6  , 6  ) E’(2, 2) 1 3 F(9, 3) F’(9  , 3  ) F’(3, 1) 1 3 The vertices of the image are D’(1, 1), E’(2, 2), and F’(3, 1).

Check It Out: Example 3A Find the vertices of the image of each figure after a dilation by the given scale factor. Then draw the image. 1 3 Scale factor

Check It Out: Example 3B Find the vertices of the image of each figure after a dilation by the given scale factor. Then draw the image. 1 4 Scale factor