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 2 right and 1 down
- A 90° counterclockwise turn about the origin, then a slide 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 7 right and 3 down
- A slide 1 right and 3 down, then a flip across the y-axis
- 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
Coordinate grid, all four quadrants, 20 squares across. Jun moved a triangle on a grid with two moves in a row. Which two moves, in order, carry it onto its image?
- A slide 1 left and 6 up, then a 180° turn about the origin
- A 180° turn about the origin, then a slide 1 left and 6 up
- A 180° turn about the origin, then a slide 5 left and 8 up
- A 90° counterclockwise turn about the origin, then a slide 1 left and 6 up
Luz 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 = x, then a slide 1 left and 4 down
- 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 2 left and 3 down
- A flip across the line y = -x, then a slide 2 left and 3 down
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. Ari's tile pattern uses a glide reflection: a slide along the mirror line y = k, then a flip across it. Corner P(2, -4) lands on P′(-5, 6). 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?
- 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
- Different: image 1 is 12 units to the left of image 2
- Different: image 1 is 12 units to the right of image 2
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?
- AB = DE again: it already put A on D, so it also puts C on F
- BC = EF alone: equal lengths put C exactly on F
- ∠B = ∠E alone: equal angles put C exactly on F
- ∠B = ∠E puts C on ray EF, and BC = EF stops C at F
Kira moves △ABC so A lands on D and B on E, with C on the same side of DE as F. Which facts put C exactly on F?
- ∠A = ∠D alone: C is on ray DF, which is enough to fix C at F
- Both angle pairs: C is on ray DF and on ray EF, and those rays meet only at F
- AB = DE again: it already put A on D and B on E, so C follows
- ∠C = ∠F: the third angles are equal, so C lands on F