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 180° rotation about the originof 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 180°:(-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 thestatement made by the teacher is inaccurate.Which best explains Kwame's solution?

Answer 1

(Reminder: To find the reflection over the x-axis, we just need to switch the signal of the y-coordinate of the points.

To find the reflection over the y-axis, we just need to switch the signal of the x-coordinate of the points)

Kwame's solution has a mistake in step 3:

The figure from step 2 is:

(1, -2), (1, -4), (2, -3).

Then, when reflecting these points over the y-axis, the result is:

(-1, -2), (-1, -4), (-2, -3)

At this point Kwame wrote (-1,2), (-1, 4), (-2, 3), which is incorrect.

Step 4 is correct, then when comparing the images in step 5, the vertices will be located in the same place, therefore the statement made by the teacher is accurate.