Problem

Are these figures congruent by a translation? Compare preimage vertices \(0,~0\); \(3,~0\); \(0,~2\) with image vertices \(5,~-1\); \(8,~-1\); \(5,~1\).

Source and image triangles: (0,0),(3,0),(0,2) correspond to (5,-1),(8,-1),(5,1).

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What this problem is really about

One matching vertex pair can suggest a translation, but congruence requires the same rigid motion to carry the whole figure. Find a candidate displacement from corresponding points, test it independently on every remaining pair, and only then use the fact that translations preserve all lengths and angles.

Answer choices

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No, the figures are not congruent because a translation cannot make the figures match exactly.

No, the figures are not congruent because checking one vertex pair is not enough to show that all the vertices use one common vector.

Yes, the figures are congruent because the translation vector is ⟨3,2⟩ from one vertex to another.

Yes, the figures are congruent because each vertex moves by the same translation vector ⟨5,-1⟩.

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Are these figures congruent by a translation? Compare preimage vertices \(0,~0\); \(3,~0\); \(0,~2\) with image vertices \(5,~-1\); \(8,~-1\); \(5,~1\).

What this problem is really about

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