What stays the same? Rigid motions and congruent shapes

Answer Key - Grade 8 Math Worksheet

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 kite drawing and its image are both drawn.

2. 1.

   Kira turns a kite drawing 90° counterclockwise about the origin. Is the image congruent to the original kite drawing?

   • No: every side changes length.
   • No: it is in a new place on the grid.
   • No: it faces a different way, so it is a different shape.
   • Yes: every side and angle stays the same size.

3. Use this

   Coordinate grid, all four quadrants, each square one unit, 20 squares across (-10 to 10), origin in the middle.

4. 2.

   Luz flips a butterfly drawing across the x-axis, like a mirror. Is the image congruent to the original butterfly drawing?

   • No: it is in a new place on the grid.
   • No: it faces a different way, so it is a different shape.
   • Yes: every side and angle stays the same size.
   • No: every side changes length.
5. 3.

   Milo enlarges a house drawing with scale factor 2 about the origin. Is the image congruent to the original house drawing?

   • Yes: every side and angle stays the same size.
   • No: every side changes length.
   • No: it is in a new place on the grid.
   • No: it faces a different way, so it is a different shape.
6. 4.

   Noah makes a poster of a boat drawing with scale factor 3 about the origin. Is the image congruent to the original boat drawing?

   • No: every side changes length.
   • Yes: every side and angle stays the same size.
   • No: it faces a different way, so it is a different shape.
   • No: it is in a new place on the grid.
8. 5.

   Ren's rocket design moved on the grid. Corner D went from (3, 1) to (-1, 3), and F went from (5, 2) to (-2, 5). Which single move was it?

   • a slide 4 units left and 2 units up
   • a turn of 180° about the origin
   • a turn of 90° counterclockwise about the origin
   • a flip across the y-axis
9. 6.

   Zee's leaf design moved on the grid. Corner D went from (-3, 4) to (3, 4), and F went from (-1, 2) to (1, 2). Which single move was it?

   Use the picture in question 5.

   • a flip across the y-axis
   • a slide 6 units right
   • a turn of 90° clockwise about the origin
   • a dilation with scale factor 2 about the origin
10. 7.

    Ari's car design moved on the grid. Corner D went from (2, 3) to (4, 6), and F went from (1, -2) to (2, -4). Which single move was it?

    Use the picture in question 5.

    • a turn of 180° about the origin
    • a flip across the x-axis
    • a slide 2 units right and 3 units up
    • a dilation with scale factor 2 about the origin

11. Use this

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

12. 8.

    Bo turns a bike sticker 90° counterclockwise about the origin. Side CD went from (1, 2) and (1, 7) to C′(-2, 1) and D′(-7, 1). How long is C′D′, in units?

    5

13. Use this

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

14. 9.

    Jun turns a plane sticker 90° clockwise about the origin. Side UV went from (3, 1) and (3, 5) to U′(1, -3) and V′(5, -3). How long is U′V′, in units?

    4

15. Use this

    Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The window drawing with sides CD and FG marked parallel; the image is not drawn.

16. 10.

    Sides CD and FG of Luz's window drawing are parallel. Luz turns it 90° counterclockwise about the origin. What is true about C′D′ and F′G′?

    • C′D′ and F′G′ are still parallel.
    • C′D′ and F′G′ are parallel, but each is now shorter.
    • C′D′ and F′G′ now cross each other.