What stays the same? Rigid motions and congruent shapes
Grade 8 Math Worksheet
Circle the best answer, or write your answer on the line.
Read this first
Use this
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 faces a different way, so it is a different shape.
- Yes: every side and angle stays the same size.
- No: every side changes length.
- No: it is in a new place on the grid.
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: it is in a new place on the grid.
- No: it faces a different way, so it is a different shape.
- No: every side changes length.
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 turn of 180° about the origin
- a slide 8 units left and 2 units down
- a dilation with scale factor 2 about the origin
- a flip across the x-axis
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 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
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 slide 2 units right and 3 units up
- a flip across the x-axis
- a dilation with scale factor 2 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?
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.
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?
Use this
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′ now cross each other.
- C′D′ and F′G′ are parallel, but each is now shorter.
- 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 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′ are still parallel.
- C′D′ and F′G′ now cross each other.
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′ now cross each other.
- C′D′ and F′G′ are still parallel.
- C′D′ and F′G′ are parallel, but each is now shorter.