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M1-041-A03-V03
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G-CO.6
Warmup
M1-041-A03-V03
Use rigid motions to transform figures and decide whether two figures are congruent.
Decide congruence by verifying a rotation
Problem
Are these figures congruent after a \(90^{\circ}\) clockwise rotation about the origin? Compare preimage vertices \((1,2)\), \((3,2)\), \((1,5)\) with image vertices \((2,-1)\), \((2,-3)\), and \((5,-1)\).
Answer choices
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A
Yes, because a rotation preserves size and shape, so the figures must be congruent even without checking whether the vertices match.
B
Yes, because a 90-degree clockwise rotation uses (x, y) to (y, -x), and (1, 2) goes to (2, -1), (3, 2) goes to (2, -3), and (1, 5) goes to (5, -1), which all match the listed image points.
C
No, because a 90-degree clockwise rotation uses (x, y) to (-y, x), so the points would not land on the listed image vertices.
D
No, because a 90-degree clockwise rotation uses (x, y) to (y, x), so the signs do not change correctly and the points do not match.
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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 by verifying a rotation
