Enlarge and shrink from the origin with any scale factor

Answer Key - Grade 8 Math Worksheet - Challenge Me

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

1. 1.

   Noah dilated a tent sticker from the origin with scale factor 4/3. Now corner D′ is at (-8, 4). Where was D before? Write it like (7, -3).

   (-6, 3)

2. 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 is drawn with C, C′ and D labeled; D′ is not drawn.

3. 2.

   Pia dilates a star design from the origin. Corner C(4, -2) lands at (6, -3). Where does corner D(-6, 6) land? Write it like (7, -3).

   (-9, 9)
4. 3.

   Ren dilates a butterfly design from the origin. Corner C(9, 3) lands at (6, 2). Where does corner D(-3, 6) land? Write it like (7, -3).

   (-2, 4)
5. 4.

   Tala dilates a snowman design from the origin. Corner C(2, -2) lands at (5, -5). Where does corner D(-4, 2) land? Write it like (7, -3).

   (-10, 5)

6. 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 image are both drawn, with C, C′, D and D′ labeled.

7. 5.

   Ari's quilt design moved. Corner C went from (2, 4) to (3, 6), and D went from (-4, 2) to (-6, 3). Is it a dilation from the origin?

   • Yes: a dilation with scale factor 2/3.
   • Yes: a dilation with scale factor 3/2.
   • No: the corners do not all multiply by the same number.
   • No: a dilation must make a shape bigger.
8. 6.

   Bo's leaf design moved. Corner C went from (6, 3) to (4, 2), and D went from (-3, 9) to (-2, 6). Is it a dilation from the origin?

   • No: the corners do not all multiply by the same number.
   • No: a dilation must make a shape bigger.
   • Yes: a dilation with scale factor 2/3.
   • Yes: a dilation with scale factor 3/2.
9. 7.

   Esme's crown design moved. Corner C went from (4, 2) to (6, 3), and D went from (2, 6) to (4, 8). Is it a dilation from the origin?

   • Yes: a dilation with scale factor 2/3.
   • No: the corners do not all multiply by the same number.
   • Yes: a dilation with scale factor 3/2.
   • No: a dilation must make a shape bigger than the original.
10. 8.

    Jun's car design moved. Corner C went from (6, 9) to (4, 6), and D went from (3, -6) to (1, -8). Is it a dilation from the origin?

    • No: a dilation must make a shape bigger.
    • Yes: a dilation with scale factor 2/3.
    • Yes: a dilation with scale factor 3/2.
    • No: the corners do not all multiply by the same number.

11. Use this

    Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The drawing and its image are both drawn, with CD and C′D′ labeled.

12. 9.

    Side CD of Kira's rocket runs from (-2, 4) to (4, 4). After a dilation from the origin, C′D′ runs from (-3, 6) to (6, 6). What is the scale factor from old to new?

    3/2
13. 10.

    Side CD of Luz's house runs from (-6, 3) to (3, 3). After a dilation from the origin, C′D′ runs from (-4, 2) to (2, 2). What is the scale factor from old to new?

    2/3