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M1-041-A04-V04
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G-CO.6
Warmup
M1-041-A04-V04
Use rigid motions to transform figures and decide whether two figures are congruent.
Decide congruence using a rigid-motion sequence
Problem
Do these figures match after this rigid-motion sequence: rotate \(90^{\circ}\) counterclockwise about the origin, then translate by \(<5,-1>\)? Compare preimage vertices \((2,1)\), \((4,1)\), and \((2,3)\) with image vertices \((4,1)\), \((4,3)\), and \((2,1)\).
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A
Yes, because rotating the preimage 90° counterclockwise about the origin gives (-1,2), (-1,4), and (-3,2), and translating those by <5,-1> gives (4,1), (4,3), and (2,1), which match the image.
B
No, because a 90° counterclockwise rotation about the origin sends (x,y) to (-x,y), so the transformed points would not match the image.
C
No, because if you translate by <5,-1> first and then rotate 90° counterclockwise about the origin, the points do not land on the listed image.
D
No, because rotating the preimage 90° clockwise about the origin gives (1,-2), (1,-4), and (3,-2), so the figures do not match after the translation.
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Curriculum context
Standard G-CO.6
Category Geometry
Domain Congruence
Objective Use rigid motions to transform figures and decide whether two figures are congruent.
Problem type Decide congruence using a rigid-motion sequence
