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M1-041-A04-V02
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G-CO.6
Warmup
M1-041-A04-V02
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 \(180\) degrees about the origin, then translate by \(<1,0>\)? Compare preimage vertices \((0,0)\), \((2,0)\), and \((0,1)\) with image vertices \((1,0)\), \((-1,0)\), and \((1,-1)\).
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A
Yes, because rotating the preimage 180° about the origin gives (0,0), (-2,0), and (0,-1), and translating those by <1,0> gives (1,0), (-1,0), and (1,-1), which match the image.
B
No, because a 180° rotation about the origin changes only the x-coordinates, so the points would not land on the listed image after the translation.
C
No, because you should translate the preimage by <1,0> first and then rotate 180° about the origin, and those points do not match the image.
D
No, because rotating the preimage 180° about the origin gives (0,0), (-2,0), and (0,-1), which do not match the image points.
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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
