What stays the same? Rigid motions and congruent shapes
Grade 8 Math Worksheet - Challenge Me
Circle the best answer, or write your answer on the line.
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Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The sticker and its final image are both drawn, with D, D′, F and F′ labeled; the middle step is not drawn.
Luz's rocket sticker moved twice. Corner D went from (2, 1) to (1, 1), and F went from (4, 5) to (-1, 5). Which moves, in order, did it?
- a slide 3 units right, then a flip across the y-axis
- a slide 1 unit left
- a turn of 180° about the origin, then a slide 3 units right
- a flip across the y-axis, then a slide 3 units right
Milo's kite sticker moved twice. Corner D went from (3, 1) to (-1, 5), and F went from (4, -2) to (2, 6). Which moves, in order, did it?
- a slide 2 units up, then a turn of 90° counterclockwise about the origin
- a turn of 90° clockwise about the origin, then a slide 2 units up
- a turn of 90° counterclockwise about the origin, then a slide 2 units up
- a slide 4 units left and 4 units up
Noah's boat sticker moved twice. Corner D went from (2, 3) to (2, -1), and F went from (6, 4) to (6, -2). Which moves, in order, did it?
- a flip across the y-axis, then a slide 2 units up
- a slide 4 units down
- a slide 2 units up, then a flip across the x-axis
- a flip across the x-axis, then a slide 2 units up
On Tala's rocket sticker, C is 5 units straight above D. After a turn of 90° counterclockwise about the origin, D′ is at (-2, 3). Where is C′? Write it like (7, -3).
On Zee's butterfly sticker, C is 4 units straight above D. After a flip across the x-axis, D′ is at (5, -2). Where is C′? Write it like (7, -3).
On Ari's leaf sticker, C is 3 units to the right of D. After a flip across the y-axis, D′ is at (-4, 6). Where is C′? Write it like (7, -3).
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Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The sticker with C, D and F labeled and a curved arrow showing clockwise; the image is not drawn.
On Luz's bike sticker, corners C, D and F go around clockwise. Luz gives the sticker a half turn (180°) about the origin. Which way do C′, D′ and F′ go around?
- it depends on how far the sticker moves
- clockwise, the same way as before
- counterclockwise, the other way
neither image is drawn. Side DF of Milo's castle picture is 4 units long. Milo dilates it with scale factor 3 about the origin, then slides it 2 units right. How long is D′F′?
Side DF of Noah's house picture is 7 units long. Noah slides it 4 units up, then dilates it with scale factor 2 about the origin. How long is D′F′?
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Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. Side DF of the robot picture is marked; neither image is drawn.
Side DF of Pia's robot picture is 7 units long. Pia flips it across the y-axis, then slides it 2 units up. How long is D′F′?