Triangle XYZ has vertices cap x times open paren 1 comma 3 close paren , cap y times open paren 0 comma 0 close paren , and cap z times open paren negative 1 comma 2 close paren The image of triangle XYZ after a rotation has vertices cap x prime times open paren negative 3 comma 1 close paren , cap y prime times open paren 0 comma 0 close paren , and cap z prime times open paren negative 2 comma negative 1 close paren Which rule describes the transformation?
Answer
A
cap r sub 0 comma 360 degrees
B
cap r sub 0 comma 180 degrees
C
cap r sub 0 comma 270 degrees
D
cap r sub 0 comma 90 degrees
Explanation
A 90-degree counterclockwise rotation about the origin follows the rule (x, y) → (−y, x). Applying it to X(1, 3) gives (−3, 1), and applying it to Z(−1, 2) gives (−2, −1), matching the image vertices. Therefore, the transformation is a 90-degree rotation about the origin, choice D.
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