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

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

   • a slide 3 units left and 2 units up, then a dilation by 1/2 from the origin
   • a slide 5 units left and 1 unit up
   • a dilation by 2 from the origin, then a slide 3 units left and 2 units up
   • a dilation by 1/2 from the origin, then a slide 3 units left and 2 units up
6. 5.

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

   (-4, 2)
7. 6.

   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)
8. 7.

   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)
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.

    Kira dilates a rain umbrella picture by 3/4 from the origin, then flips it across the y-axis. DF was 8 units and ∠D was 110°. What are D′F′ and ∠D′? Type: length, angle.

    6, 110