Question

Figure G is rotated 90degree clockwise about the origin and then reflected over the x-axis, forming figure H.

On a coordinate plane, triangle G has points (negative 3, 1), (negative 1, 2), (negative 2, 5). Triangle H has points (2, negative 1), (1, negative 3), (5, negative 2).

Which sequence of transformations will produce the same results?
a reflection over the y-axis and then a rotation 90degree clockwise about the origin
a reflection over the x-axis and then a rotation 90degree clockwise about the origin
a 180degree rotation about the origin
a reflection over the y-axis and then a reflection over the x-axis

Answer 1

Answer: a reflection over the y-axis and then a rotation 90° clockwise about the origin.

Reason: The given sequence (rotate 90° clockwise then reflect over the x-axis) maps (x,y) -> (y,-x) -> (y,x). A reflection over the y-axis followed by a 90° clockwise rotation maps (x,y) -> (-x,y) -> (y,x) as well, so the two sequences are equivalent.