Similar shapes: a dilation plus moves

Answer Key - Grade 8 Math Worksheet - Challenge Me

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

1. Read this first

   Use this

   Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The design and its copy are both drawn, with D, D′, F and F′ labeled; the middle step is not drawn.

2. 1.

   Kira's kite design became a similar copy. D went from (1, 2) to (8, 4), and F from (1, -2) to (8, -4). Which moves did it, in order?

   • a dilation by 2 from the origin, then a slide 3 units right
   • a slide 7 units right and 2 units up
   • a slide 3 units right, then a dilation by 1/2 from the origin
   • a slide 3 units right, then a dilation by 2 from the origin
3. 2.

   Luz's rocket design became a similar copy. D went from (2, 4) to (3, 3), and F from (4, -2) to (6, -6). Which moves did it, in order?

   • a dilation by 3/2 from the origin, then a slide 2 units down
   • a slide 1 unit right and 1 unit down
   • a slide 2 units down, then a dilation by 2/3 from the origin
   • a slide 2 units down, then a dilation by 3/2 from the origin
4. 3.

   Milo's boat design became a similar copy. D went from (2, 3) to (-3, 6), and F from (1, -2) to (-1, -4). Which moves did it, in order?

   • a dilation by 2 from the origin, then a flip across the y-axis, then a slide 1 unit right
   • a slide 5 units left and 3 units up
   • a dilation by 1/2 from the origin, then a flip across the y-axis, then a slide 1 unit right
   • a slide 1 unit right, then a dilation by 2 from the origin, then a flip across the y-axis
5. 4.

   Pia dilated a star sticker by 2 from the origin, then slid it 2 units right and 3 units down. D′ is now at (6, 1). Where did D start? Write it like (7, -3).

   (2, 2)
6. 5.

   Tala dilated a kite sticker by 1/2 from the origin, then slid it 2 units right and 4 units down. D′ is now at (4, -6). Where did D start? Write it like (7, -3).

   (4, -4)
7. 6.

   Zee dilated a butterfly sticker by 3 from the origin, then slid it 3 units right and 4 units down. D′ is now at (9, 5). Where did D start? Write it like (7, -3).

   (2, 3)
8. 7.

   Ari dilates a castle picture from the origin by 2, then dilates the copy by 3/4. One dilation from the origin would do both. What is its scale factor?

   3/2
9. 8.

   Bo dilates a robot picture from the origin by 4, then dilates the copy by 1/2. One dilation from the origin would do both. What is its scale factor?

   2
10. 9.

    Jun dilates a kite picture by 2 from the origin, then turns it 90° counterclockwise. DF was 5 units and ∠D was 64°. What are D′F′ and ∠D′? Type: length, angle.

    10, 64
11. 10.

    Luz dilates a sled picture by 5/2 from the origin, then slides it 3 units right. DF was 4 units and ∠D was 35°. What are D′F′ and ∠D′? Type: length, angle.

    10, 35