Question

in trapezoid wxyz, $overline{wx}$ is parallel to $overline{zy}$. trapezoid $wxyz$ is the image of trapezoid wxyz under a translation along $overrightarrow{xy}$. which statements about trapezoid $wxyz$ are true? select all that apply. the measure of $angle xyz$ is 90 degree. the measure of $angle wzy$ is 90 degree. the length of $overline{zy}$ is 2 u. the length of $overline{wx}$ is 2 units. $overline{wx}$ is parallel to $overline{zy}$. $overline{wz}$ is parallel to $overline{xy}$

Explanation:

Step1: Recall translation property

A translation is a rigid - motion. It preserves side - lengths and angle - measures.

Step2: Analyze angle measures

In trapezoid \(WXYZ\), assume \(\angle WZY = 90^{\circ}\). Since translation preserves angle - measures, \(\angle W'Z'Y'=\angle WZY = 90^{\circ}\). And there is no indication that \(\angle X'Y'Z' = 90^{\circ}\) in the original trapezoid, so we cannot say \(\angle X'Y'Z'=90^{\circ}\).

Step3: Analyze side - lengths

If \(WX = 2\) units and \(ZY=3\) units in trapezoid \(WXYZ\), then \(W'X'=WX = 2\) units and \(Z'Y'=ZY = 3\) units.

Step4: Analyze parallel sides

If \(\overline{WX}\parallel\overline{ZY}\) in trapezoid \(WXYZ\), then \(\overline{W'X'}\parallel\overline{Z'Y'}\) because translation preserves parallelism. And there is no indication that \(\overline{W'Z'}\parallel\overline{X'Y'}\) in the original trapezoid.

Answer:

The measure of \(\angle W'Z'Y'\) is \(90\) degrees, The length of \(\overline{W'X'}\) is \(2\) units, \(\overline{W'X'}\) is parallel to \(\overline{Z'Y'}\)