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M1-041-A02-V02
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G-CO.6
Warmup
M1-041-A02-V02
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 the \(x\text{-}\text{axis}\)? Compare preimage vertices \((2,3)\), \((5,3)\), \((2,7)\) with image vertices \((2,-3)\), \((5,-3)\), and \((2,-6)\).
Answer choices
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A
Yes, the figures are congruent because all the coordinates use the same numbers with opposite signs, so the reflected triangle matches.
B
No, the figures are not congruent because reflecting across the x-axis sends (2,7) to (2,-7), not to the listed point (2,-6).
C
No, the figures are not congruent because a reflection across the x-axis should change the x-values, but these x-values stay the same.
D
Yes, the figures are congruent because the first two vertices reflect correctly across the x-axis, so the whole figure must 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 reflection
