Question

What series of transformations would carry the trapezoid onto itself?

these are the answers
(x + 0, y − 4), 90° clockwise rotation, reflection over the y-axis
(x + 0, y − 4), 180° rotation, reflection over the y-axis
(x + 6, y + 0), 90° clockwise rotation, reflection over the x‐axis
(x + 6, y + 0), 180° rotation, reflection over the x‐axis

Answer 1

(x + 6, y + 0), 180° rotation, reflection over the x‐axis

Explanation:

Answer 2

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Answer:

(x + 6, y + 0), 180° rotation, reflection over the x‐axis

Explanation:

A rotation 90° and a reflection over an axis will result in a figure 90° rotated from the one shown. That rotation cannot be part of the answer.

If reflection is to be over the y-axis after a rotation of 180°, the translation must amount to a reflection over the x-axis. That is not possible with this shape.

However, translating to the right, in to the first quadrant can be effectively a reflection over the y-axis. Then 180° rotation and reflection over the x-axis will map the figure to itself. This set of transformations is described in the last answer choice:

(x + 6, y + 0), 180° rotation, reflection over the x‐axis