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: it is in a new place on the grid.
   • 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.

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

   • No: it faces a different way, so it is a different shape.
   • No: every side changes length.
   • Yes: every side and angle stays the same size.
   • No: it is in a new place on the grid.
7. 4.

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

   • a slide 8 units left and 2 units down
   • a dilation with scale factor 2 about the origin
   • a flip across the x-axis
   • a turn of 180° about the origin
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?

   Use the picture in question 4.

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

   Tala's umbrella design moved on the grid. Corner D went from (2, 5) to (2, -5), and F went from (6, 1) to (6, -1). Which single move was it?

   Use the picture in question 4.

   • a turn of 180° about the origin
   • a slide 10 units down
   • a flip across the x-axis
   • 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 4.

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

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 sticker and its image are both drawn, with Q, S, Q′ and S′ labeled.

16. 10.

    Kira turns a turtle sticker 90° clockwise about the origin. Side QS went from (-2, 4) and (-2, 7) to Q′(4, 2) and S′(7, 2). How long is Q′S′, in units?

    3