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M1-041-A02-V03
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G-CO.6
Warmup
M1-041-A02-V03
Use rigid motions to transform figures and decide whether two figures are congruent.
Decide congruence by verifying a reflection
Problem
Are these figures congruent after a reflection across \(x=1\)? Compare preimage vertices \((3,0)\), \((5,2)\), \((3,4)\) with image vertices \((-1,0)\), \((-3,2)\), and \((-1,4)\).
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A
No, the figures are not congruent because a reflection should send (3,0) to (-3,0) and (5,2) to (-5,2), so the listed image does not match.
B
Yes, the figures are congruent because the image points have the same y-values and similar x-values, so the triangle must be a correct reflection.
C
No, the figures are not congruent because reflecting across x=1 should keep the x-values the same, but these points have different x-coordinates.
D
Yes, the figures are congruent because reflecting across x=1 keeps y the same and sends (3,0), (5,2), and (3,4) to (-1,0), (-3,2), and (-1,4).
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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 reflection
