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.

2. 1.

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

   • No: every side changes length.
   • No: it is in a new place on the grid.
   • Yes: every side and angle stays the same size.
   • No: it faces a different way, so it is a different shape.
3. 2.

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

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

   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 turn of 180° about the origin
   • a dilation with scale factor 2 about the origin
   • a flip across the x-axis
6. 4.

   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 3.

   • a flip across the y-axis
   • a turn of 90° counterclockwise about the origin
   • a slide 4 units left and 2 units up
   • a turn of 180° about the origin
7. 5.

   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 3.

   • a flip across the x-axis
   • a turn of 180° about the origin
   • a slide 10 units down
   • a dilation with scale factor 2 about the origin
8. 6.

   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 3.

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

9. 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.

10. 7.

    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
11. 8.

    Coordinate grid, all four quadrants, each square one unit, 20 squares across (-10 to 10), origin in the middle. Esme turns a sled sticker 90° counterclockwise about the origin. Side FG went from (2, 3) and (2, 9) to F′(-3, 2) and G′(-9, 2). How long is F′G′, in units?

    6

12. 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.

13. 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

14. 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.

15. 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