Problem

Are these figures congruent after a reflection across the \(y\text{-}\text{axis}\)? Compare preimage vertices \((1,2)\), \((4,2)\), \((1,5)\) with image vertices \((-1,2)\), \((-4,2)\), and \((-1,5)\).

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What this problem is really about

A proposed reflection proves congruence only when one mirror rule works for every corresponding point. Translate the vertical-axis mirror into its coordinate effect, audit all labeled pairs under that same rule, and then connect an exact match to the reflection’s preservation of distances and angle measures.

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Yes, the figures are congruent because the coordinates use the same numbers, just in a different order, so the triangles must match.

No, the figures are not congruent because reflections move points to opposite quadrants, but these points keep the same y-values.

Yes, the figures are congruent because each point follows the rule (x, y) -> (-x, y), so only the x-value changes sign.

No, the figures are not congruent because a reflection across the y-axis should change the y-values instead of the x-values.

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Are these figures congruent after a reflection across the \(y\text{-}\text{axis}\)? Compare preimage vertices \((1,2)\), \((4,2)\), \((1,5)\) with image vertices \((-1,2)\), \((-4,2)\), and \((-1,5)\).

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