Question

A teacher asks students to determine the accuracy of this statement.

A reflection over the x-axis and then over the y-axis results in the same transformation as a 180degree rotation about the origin of the original figure.

Kwame’s explanation of the accuracy of the statement is shown below.

Step 1: Choose the vertices of a pre-image: (1, 2), (1, 4), (2, 3).
Step 2: Reflect the pre-image over the x-axis: (1, –2), (1, –4), (2, –3).
Step 3: Reflect the figure from step 2 over the y-axis: (–1, 2), (–1, 4), (–2, 3).
Step 4: Rotate the pre-image 180degree: (–1, –2), (–1, –4), (–2, –3).
Step 5: Compare the reflected figure to the rotated figure. The vertices are not located in the same place, therefore the statement made by the teacher is inaccurate.

Which best explains Kwame’s solution?
Kwame’s explanation and solution are incorrect. He reflected the image over the y-axis in step 2 and the x-axis in step 3, instead of the reverse.
Kwame’s explanation and solution are incorrect. He reflected the pre-image at step 3, rather than the figure from step 2.
Kwame’s explanation and solution are incorrect. When reflecting over the x- and y-axes, he negated the incorrect coordinate in the ordered pair.
Kwame’s explanation and solution are incorrect. The coordinates of the rotated figure should be switched and negated, not just negated.

Answer 1

Kwame’s explanation and solution are incorrect. He reflected the pre-image at step 3, rather than the figure from step 2.

(After reflecting over the x-axis he should have reflected (1, −2), (1, −4), (2, −3) over the y‑axis to get (−1, −2), (−1, −4), (−2, −3), which matches the 180° rotation.)