Questions: Figure G is rotated 90 clockwise about the origin and then reflected over the x-axis, forming figure H. Which sequence of transformations will produce the same results? a reflection over the y-axis and then a rotation 90° clockwise about the origin a reflection over the x-axis and then a rotation 90 clockwise about the origin

Solution Steps

Figure G is rotated 90° clockwise about the origin. This maps: (-2, 5) -> (5, 2) (-3, 1) -> (1, 3) (-1, 2) -> (2, 1)

Then, it's reflected over the x-axis. This maps: (5, 2) -> (5, -2) (1, 3) -> (1, -3) (2, 1) -> (2, -1)

These final coordinates match figure H.

A reflection over the y-axis maps: (-2, 5) -> (2, 5) (-3, 1) -> (3, 1) (-1, 2) -> (1, 2)

Then a 90° clockwise rotation about the origin maps: (2, 5) -> (5, -2) (3, 1) -> (1, -3) (1, 2) -> (2, -1)

These final coordinates match figure H.

A reflection over the x-axis maps: (-2, 5) -> (-2, -5) (-3, 1) -> (-3, -1) (-1, 2) -> (-1, -2)

Then a 90° clockwise rotation about the origin maps: (-2, -5) -> (-5, 2) (-3, -1) -> (-1, 3) (-1, -2) -> (-2, 1)

These final coordinates do _not_ match figure H.

Final Answer