What stays the same? Rigid motions and congruent shapes

Answer Key - Grade 8 Math Worksheet - Building Confidence

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 bus sticker with side FG marked and an arrow 4 units down; the image is not drawn. Table side | length: FG | 7; F′G′ | ?

2. 1.

   Bo slides a bus sticker 4 units down. Side FG is 7 units long, and the table row is FG | F′G′ = 7 | ?. How long is F′G′?

   7

3. Use this

   Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The castle sticker with side DH marked and an arrow 7 units left; the image is not drawn. Table side | length: DH | 5; D′H′ | ?

4. 2.

   Esme slides a castle sticker 7 units left. Side DH is 5 units long, and the table row is DH | D′H′ = 5 | ?. How long is D′H′?

   5
5. 3.

   Side FG of Luz's tent drawing goes from F(3, 2) to G(3, 9). Luz slides the drawing 5 units left. How long is F′G′, in units?

   7
6. 4.

   Side UV of Milo's house drawing goes from U(-4, 3) to V(-4, 8). Milo slides the drawing 2 units down. How long is U′V′, in units?

   5
7. 5.

   Side QS of Noah's ladder drawing goes from Q(1, 3) to S(1, 8). Noah slides the drawing 2 units up. How long is Q′S′, in units?

   5
8. 6.

   Pia turns a kite sticker 90° counterclockwise about the origin. Angle D on the sticker is 48°, and the table row is ∠D | ∠D′ = 48° | ?. What is ∠D′, in degrees?

   48

9. Use this

   Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The boat sticker with ∠F marked and a curved arrow 180° about the origin; the image is not drawn. Table angle | size: ∠F | 65°; ∠F′ | ?

10. 7.

    Ren turns a boat sticker 180° about the origin. Angle F on the sticker is 65°, and the table row is ∠F | ∠F′ = 65° | ?. What is ∠F′, in degrees?

    65
11. 8.

    D(4, 2) | D′(-2, 4); F(1, 5) | F′(-5, 1). Ari's table for a butterfly design: D(4, 2) → (-2, 4) and F(1, 5) → (-5, 1). Both rows fit (x, y) → (−y, x). Which move is it?

    • a flip across the y-axis
    • a turn of 90° counterclockwise about the origin
    • a slide 6 units left and 2 units up
    • a dilation with scale factor 2 about the origin
12. 9.

    D(3, 4) | D′(3, -4); F(6, 1) | F′(6, -1). Esme's table for a quilt design: D(3, 4) → (3, -4) and F(6, 1) → (6, -1). Both rows fit (x, y) → (x, −y). Which move is it?

    • a dilation with scale factor 2 about the origin
    • a slide 8 units down
    • a flip across the x-axis
    • a turn of 90° clockwise about the origin
13. 10.

    D(-2, 5) | D′(2, 5); F(-6, 3) | F′(6, 3). Jun's table for a snowflake design: D(-2, 5) → (2, 5) and F(-6, 3) → (6, 3). Both rows fit (x, y) → (−x, y). Which move is it?

    • a flip across the y-axis
    • a turn of 180° about the origin
    • a slide 4 units right
    • a dilation with scale factor 2 about the origin