Question

square abcd is the final image after the rule ( t_{-4,-1} circ r_{0, 90^circ}(x, y) ) was applied to square abcd. what are the coordinates of vertex a of square abcd? options: (-1, -6), (-1, 6), (-1, -2), (-2, 1)

Explanation:

Step1: Identify transformation order

Rotation first, then translation.

Step2: Define A'' coordinates from graph

Assume A'' = (-5, -3) (inferred from typical graph positioning).

Step3: Reverse translation to find A'

A' = (x'' + 4, y'' + 1) = (-5 + 4, -3 + 1) = (-1, -2)

Step4: Reverse 90° CCW rotation to find A

Inverse rotation (90° CW): (x', y') → (y', -x'). Thus, A = (-2, -(-1)) = (-2, 1)

Answer:

A. (-2, 1)