Question

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 the statement made by the teacher is incorrect. 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 coordinates of the ordered pair. kwame’s explanation and solution are incorrect. the coordinates of the rotated figure should be switched and negated, not just negated.

Explanation:

First, recall the rules for transformations:

1. Reflecting a point $(x,y)$ over the x-axis gives $(x,-y)$.
2. Reflecting a point $(x,y)$ over the y-axis gives $(-x,y)$.
3. Rotating a point $(x,y)$ 180° gives $(-x,-y)$.

Kwame's Step 2 correctly reflects over the x-axis to get $(1,-2), (1,-4), (2,-3)$. But in Step 3, he should reflect the result of Step 2 over the y-axis: reflecting $(1,-2)$ over y-axis is $(-1,-2)$, $(1,-4)$ becomes $(-1,-4)$, $(2,-3)$ becomes $(-2,-3)$. Instead, he incorrectly reflected the original pre-image over the y-axis, getting $(-1,2), (-1,4), (-2,3)$. This mistake means his comparison to the 180° rotation (which is $(-1,-2), (-1,-4), (-2,-3)$) is wrong because he used the wrong figure for Step 3.

Answer:

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