What stays the same? Rigid motions and congruent shapes
Grade 8 Math Worksheet
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 kite drawing and its image are both drawn.
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.
- Yes: every side and angle stays the same size.
- No: it faces a different way, so it is a different shape.
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Coordinate grid, all four quadrants, each square one unit, 20 squares across (-10 to 10), origin in the middle.
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.
- Yes: every side and angle stays the same size.
- No: it faces a different way, so it is a different shape.
- No: every side changes length.
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.
- Yes: every side and angle stays the same size.
- No: it is in a new place on the grid.
- No: it faces a different way, so it is a different shape.
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?
- a slide 6 units right
- a turn of 90° clockwise about the origin
- a dilation with scale factor 2 about the origin
- a flip across the y-axis
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 slide 2 units right and 3 units up
- a dilation with scale factor 2 about the origin
- a flip across the x-axis
- a turn of 180° about the origin
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?
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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 image are both drawn, with U, V, U′ and V′ labeled.
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?
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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.
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 parallel, but each is now shorter.
- C′D′ and F′G′ now cross each other.
- C′D′ and F′G′ are still parallel.
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Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The quilt drawing with sides CD and FG marked parallel; the image is not drawn.
Sides CD and FG of Milo's quilt square are parallel. Milo flips it across the y-axis. What is true about C′D′ and F′G′?
- C′D′ and F′G′ are parallel, but each is now shorter.
- C′D′ and F′G′ now cross each other.
- C′D′ and F′G′ are still parallel.
Use this
Coordinate grid, all four quadrants, each square one unit, 20 squares across (−10 to 10), origin in the middle. The ladder drawing with sides CD and FG marked parallel; the image is not drawn.
The two rails of Noah's ladder drawing, CD and FG, are parallel. Noah slides it 5 units left and 2 units up. What is true about C′D′ and F′G′?
- C′D′ and F′G′ are parallel, but each is now shorter.
- C′D′ and F′G′ now cross each other.
- C′D′ and F′G′ are still parallel.
