A rectangle is transformed according to the rule cap r sub 0 comma 90 degrees The image of the rectangle has vertices located at cap r prime times open paren negative 4 comma 4 close paren , cap s prime times open paren negative 4 comma 1 close paren , cap p prime times open paren negative 3 comma 1 close paren , and cap q prime times open paren negative 3 comma 4 close paren What is the location of cap q ?
Answer
A
open paren negative 4 comma negative 3 close paren
B
open paren 4 comma 3 close paren
C
open paren 3 comma 4 close paren
D
open paren negative 3 comma negative 4 close paren
Explanation
A 90° rotation about the origin maps (x, y) to (−y, x). To find the original location of Q, reverse that rotation: Q′(−3, 4) corresponds to Q(4, 3). Therefore, the location of Q is (4, 3), choice A.
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