Similar shapes: a dilation plus moves

Answer Key - Grade 8 Math Worksheet

Circle the best answer, or write your answer on the line.

1. 1.

   Bo dilates a sled sticker by 3/2 from the origin, then slides it 2 units right and 4 units down. Where does corner D(-4, 6) end? Write it like (7, -3).

   (-4, 5)
2. 2.

   Esme dilates a plane sticker by 1/2 from the origin, then slides it 5 units left and 3 units up. Where does corner D(8, -4) end? Write it like (7, -3).

   (-1, 1)
3. 3.

   Kira slides a turtle sticker 1 unit right and 2 units down, then dilates it by 3/2 from the origin. Where does corner D(5, -2) end? Write it like (7, -3).

   (9, -6)

4. Read this first

   Use this

   Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. Drawings A and B are both drawn. Table A | B: 9 | 6.

5. 4.

   Drawing B is Pia's house drawing A, dilated and turned. A's side is 9 units; B's matching side is 6 units. What is the scale factor from A to B?

   2/3
6. 5.

   Ren compares two window cards. Card A is 4 by 6 units; card B is 6 by 9 units. Can a dilation and moves take A onto B?

   • Yes: every side grows by 2 units.
   • Yes: every side is multiplied by 3/2.
   • No: the sides do not all grow by the same factor.
7. 6.

   Tala compares two quilt cards. Card A is 6 by 9 units; card B is 4 by 6 units. Can a dilation and moves take A onto B?

   • Yes: every side is multiplied by 2/3.
   • No: the sides do not all grow by the same factor.
   • Yes: every side shrinks by 2 units.

8. Use this

   Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. Cards A and B are drawn. Table A | B: 6 | 9; 8 | 11.

9. 7.

   Ari compares two quilt cards. Card A is 6 by 8 units; card B is 9 by 11 units. Can a dilation and moves take A onto B?

   • No: the sides do not all grow by the same factor.
   • Yes: every side is multiplied by 3/2.
   • Yes: every side grows by 3 units.

10. Use this

    Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. Drawings A and B are both drawn. Table A | B: 4 | 6; 14 | ?

11. 8.

    Bo's kite drawing A has sides 4 and 14 units. Drawing B is A dilated and slid. B's side matching 4 is 6 units. How long is B's side matching 14?

    21
12. 9.

    Esme's boat drawing A has sides 9 and 21 units. Drawing B is A dilated and slid. B's side matching 9 is 6 units. How long is B's side matching 21?

    14
13. 10.

    Jun's tent drawing A has sides 6 and 9 units. Drawing B is A dilated and slid. B's side matching 6 is 8 units. How long is B's side matching 9?

    12