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 180° 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 1800 (-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.
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