Sequences of transformations, including glide reflections
Grade 10 Math Worksheet
Circle the best answer, or write your answer on the line.
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Coordinate grid, all four quadrants, 20 squares across. △PQR: P(1, 1), Q(4, 1), R(1, 3). Its image: P′(1, 0), Q′(1, 3), R′(-1, 0). Both are drawn.
Bo moved a triangle on a grid with two moves in a row. Which two moves, in order, carry it onto its image?
- A slide 2 right and 1 down, then a 90° counterclockwise turn about the origin
- A 90° clockwise turn about the origin, then a slide 2 right and 1 down
- A 90° counterclockwise turn about the origin, then a slide 1 down
- A 90° counterclockwise turn about the origin, then a slide 2 right and 1 down
Coordinate grid, all four quadrants, 20 squares across. Both are drawn. Kira moved a triangle on a grid with two moves in a row. Which two moves, in order, carry it onto its image?
- A flip across the y-axis, then a slide 1 right and 3 down
- A flip across the x-axis, then a slide 1 right and 3 down
- A flip across the y-axis, then a slide 7 right and 3 down
- A slide 1 right and 3 down, then a flip across the y-axis
Luz moved a triangle on a grid with two moves in a row. Which two moves, in order, carry it onto its image?
- A slide 2 left and 3 down, then a flip across the line y = x
- A flip across the line y = x, then a slide 1 left and 4 down
- A flip across the line y = x, then a slide 2 left and 3 down
- A flip across the line y = -x, then a slide 2 left and 3 down
Coordinate grid, all four quadrants, 20 squares across. Milo moved a triangle on a grid with two moves in a row. Which two moves, in order, carry it onto its image?
- A flip across the line y = -1, then a slide 3 right and 2 down
- A flip across the line y = 1, then a slide 3 right and 2 up
- A flip across the line y = 1, then a slide 3 right and 2 down
- A slide 3 right and 2 down, then a flip across the line y = 1
Zee's tile pattern uses a glide reflection: a slide along the mirror line y = k, then a flip across it. Corner P(-2, 5) lands on P′(7, -1). What is k?
The slide length and the mirror line are not given. Noah's tile pattern uses a glide reflection: a slide along the mirror line x = k, then a flip across it. Corner P(-4, 3) lands on P′(6, 8). What is k?
Tala tests whether order matters. Image 1: flip a design across the y-axis, then slide it 6 units right. Image 2: slide first, then flip. How do the images compare?
- Different: image 1 is 12 units to the left of image 2
- Different: image 1 is 12 units to the right of image 2
- The same image, because a slide and a flip are both rigid motions
- Different: image 1 is 6 units to the right of image 2
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A design with corner (x, y). Image 1 is made by the half turn, then the flip. Image 2 is made by the flip, then the half turn.
Esme asks whether order matters for a 180° turn about the origin and a flip across the y-axis. Image 1: turn, then flip. Image 2: flip, then turn. How do the images compare?
- The same: both orders send (x, y) to (-x, -y)
- The same: both orders send (x, y) to (x, -y)
- Different: order matters when one of the moves is a flip
- Different: the two images are mirror images across the x-axis
Ren wants A to land on D, B on E and C on F, using only turns and slides. Which statement is right?
- It can be done: slide A onto D, then turn 90° counterclockwise about D
- It can be done: the three side lengths match, and turns and slides keep lengths
- It cannot be done: △DEF is bigger than △ABC
- It cannot be done: the triangles are congruent, but a flip is needed to reverse the turn direction
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AB = DE = 5 cm. ∠B = ∠E = 40°. BC = EF = 7 cm. A on D uses AB = DE.
Pia moves △ABC so B lands on E and A lands on D, flipping if needed so C is on the same side of line DE as F. Which fact puts C exactly on F?
- ∠B = ∠E puts C on ray EF, and BC = EF stops C at F
- BC = EF alone: equal lengths put C exactly on F
- ∠B = ∠E alone: equal angles put C exactly on F
- AB = DE again: it already put A on D, so it also puts C on F