Similar shapes: a dilation plus moves
Grade 8 Math Worksheet - Challenge Me
Circle the best answer, or write your answer on the line.
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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.
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 3 units right, then a dilation by 1/2 from the origin
- 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 2 from the origin
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 slide 2 units down, then a dilation by 3/2 from the origin
- a dilation by 3/2 from the origin, then a slide 2 units down
- a slide 2 units down, then a dilation by 2/3 from the origin
- a slide 1 unit right and 1 unit down
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 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
- 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
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).
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).
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?
Esme dilates a house picture from the origin by 1/2, then dilates the copy by 3. One dilation from the origin would do both. What is its scale factor?
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.
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.
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.
