Problem

Are these figures congruent after a \(90^{\circ}\) counterclockwise rotation about the origin? Compare preimage vertices \((1,0)\), \((2,0)\), \((1,3)\) with image vertices \((0,1)\), \((0,2)\), and \((-3,1)\).

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What this problem is really about

Verifying congruence by rotation has two layers: coordinate matching and rigidity. Derive the counterclockwise quarter-turn rule from the geometry, apply it to every preimage vertex, and compare labels in order; if one rotation maps the entire figure, its distance-and-angle preservation supplies the congruence argument.

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No, because a 90-degree counterclockwise rotation uses (x,y) → (-y,x), and the point (1,3) would go to (3,1), not (-3,1).

No, because a 90-degree counterclockwise rotation uses (x,y) → (y,-x), so the points would not land on the listed image vertices.

No, because the x- and y-coordinates switch places in a 90-degree counterclockwise rotation, so (1,0), (2,0), and (1,3) should become (0,1), (0,2), and (3,1).

Yes, because a 90-degree counterclockwise rotation uses (x,y) → (-y,x), and the vertices (1,0), (2,0), and (1,3) become (0,1), (0,2), and (-3,1).

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Are these figures congruent after a \(90^{\circ}\) counterclockwise rotation about the origin? Compare preimage vertices \((1,0)\), \((2,0)\), \((1,3)\) with image vertices \((0,1)\), \((0,2)\), and \((-3,1)\).

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