Question

The graph shows kites TUVW and T'U'V'W'.
TUVW Points: T (-3, -9), U (-2, -6), V (-3, -5), W (-4, -6)
T'U'V'W' Points: T' (-9, -3), U' (-6, -2), V' (-5, -3), W' (-6, -4)

Which sequence of transformations maps TUVW onto T'U'V'W'?
A. a rotation 90 degrees counterclockwise around the origin followed by a reflection across the y-axis
B. reflection across the y-axis followed by a translation left 8 units and up 2 units
C. a translation up 14 units followed by rotation 90 degrees counterclockwise around the origin

Answer 1

A.

Rotation 90° CCW about the origin sends (x,y) -> (−y,x). Reflecting across the y‑axis then sends (a,b) -> (−a,b), so the composition sends (x,y) -> (y,x).

Apply to the vertices: T(−3,−9) -> (−9,−3), U(−2,−6) -> (−6,−2), V(−3,−5) -> (−5,−3), W(−4,−6) -> (−6,−4), which matches T'U'V'W'. Options B and C do not produce these images.