Question

shonda was curious if segments \\(\overline{wx}\\) and \\(\overline{yz}\\) were congruent, so she tried to map one figure onto the other using transformations:
image of a grid with segments wx, wy, yz
shonda concluded:
\its not possible to map \\(\overline{wx}\\) onto \\(\overline{yz}\\) using a sequence of rigid transformations, so the segments are not congruent.\
what error did shonda make in her conclusion?
choose 1 answer:
a one more transformation — a rotation — would map \\(\overline{wx}\\) onto \\(\overline{yz}\\). so the segments are congruent.
b one more transformation — a reflection — would map \\(\overline{wx}\\) onto \\(\overline{yz}\\). so the segments are congruent.
c there is no error. this is a correct conclusion.

Explanation:

To determine the error in Shonda's conclusion, we analyze the rigid transformations (reflection, rotation, translation) that preserve segment length (congruence). $\overline{WX}$ and $\overline{YZ}$ have the same length (can be verified by counting grid units). A rotation can align $\overline{WX}$ (horizontal) to $\overline{YZ}$ (vertical) after initial transformations. Option A states a rotation would map $\overline{WX}$ to $\overline{YZ}$, showing they are congruent. Option B’s reflection is less likely, and Option C is incorrect as the segments are congruent.

Answer:

A. One more transformation — a rotation — would map $\overline{WX}$ onto $\overline{YZ}$. So the segments are congruent.