Similar shapes: a dilation plus moves

Answer Key - Grade 8 Math Worksheet - Building Confidence

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

1. 1.

   Ari dilates a kite sticker by 3 from the origin, then slides it 2 units right. Side DF is 5 units; the table row is 5 → 5 × 3. How long is D′F′?

   15
2. 2.

   Bo dilates a boat sticker by 3/2 from the origin, then slides it 5 units down. Side DF is 6 units; the table row is 6 → 6 × 3/2. How long is D′F′?

   9
3. 3.

   Esme dilates a rocket sticker by 1/2 from the origin, then slides it 3 units left. Side DF is 8 units; the table row is 8 → 8 × 1/2. How long is D′F′?

   4
4. 4.

   Jun dilates a star sticker by 2 from the origin, then slides it 3 units up. Side DF is 7 units; the table row is 7 → 7 × 2. How long is D′F′?

   14
5. 5.

   Kira dilates a butterfly sticker by 2 from the origin, then turns it 90° counterclockwise about the origin. ∠D is 50°; the row is ∠D | ∠D′ = 50° | ?. What is ∠D′?

   50
6. 6.

   Luz dilates a leaf sticker by 3 from the origin, then turns it 180° about the origin. ∠F is 70°; the row is ∠F | ∠F′ = 70° | ?. What is ∠F′?

   70
7. 7.

   Noah dilates a snowflake sticker by 3/2 from the origin, then flips it across the x-axis. ∠H is 40°; the row is ∠H | ∠H′ = 40° | ?. What is ∠H′?

   40

8. 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 quilt design and its copy are both drawn. Table side | length: DF | 3; D′F′ | 6.

9. 8.

   Pia dilates a quilt design by 2 from the origin, then turns it 90° about the origin. Side DF went from 3 units to 6 units. How is the copy related to the original?

   • Neither: the copy is a different shape.
   • Similar but not congruent: the same shape, a new size.
   • Congruent: the same shape and the same size, just moved.
10. 9.

    Ren dilates a crown design by 1/2 from the origin, then flips it across the y-axis. Side DF went from 8 units to 4 units. How is the copy related to the original?

    • Congruent: the same shape and the same size.
    • Neither: the copy is a different shape.
    • Similar but not congruent: the same shape, a new size.
11. 10.

    Zee flips a house design across the x-axis, then slides it 3 units left. Side DF went from 7 units to 7 units. How is the copy related to the original?

    • Similar but not congruent: the same shape, a new size.
    • Congruent: the same shape and the same size.
    • Neither: the copy is a different shape.