Problem

Do these figures match after this rigid-motion sequence: reflect over the \(y\text{-}\text{axis}\), then translate by \(<3,1>\)? Compare preimage vertices \((1,0)\), \((4,0)\), and \((1,2)\) with image vertices \((2,1)\), \((-1,1)\), and \((2,3)\).

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What this problem is really about

A rigid-motion sequence remains rigid, but its order still matters for whether it reaches the stated target. Compute and label the reflected intermediate triangle first, translate those intermediate coordinates next, and compare every final vertex with its designated image before drawing a congruence conclusion.

Answer choices

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No, because if you translate the preimage by <3,1> first and then reflect over the y-axis, the points do not land on (2,1), (-1,1), and (2,3).

Yes, because reflecting the preimage over the y-axis gives (-1,0), (-4,0), and (-1,2), and translating those by <3,1> gives (2,1), (-1,1), and (2,3), which match the image.

No, because after reflecting over the y-axis, you should translate by <-3,1> instead of <3,1>, so the figures do not match.

No, because reflecting over the y-axis makes the y-coordinates switch signs, so the reflected points would not translate to the listed image.

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Do these figures match after this rigid-motion sequence: reflect over the \(y\text{-}\text{axis}\), then translate by \(<3,1>\)? Compare preimage vertices \((1,0)\), \((4,0)\), and \((1,2)\) with image vertices \((2,1)\), \((-1,1)\), and \((2,3)\).

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