Question

the graph shows quadrilaterals abcd and wxyz. is abcd congruent to wxyz? justify your answer. yes, because a translation right 10 units followed by a reflection across the x - axis maps abcd onto wxyz. yes, because a rotation 180° around the origin maps abcd onto wxyz. no, because \\( \overline { c d } \\) and \\( \overline { y z } \\) do not have the same length. no, because \\( \angle c \\) and \\( \angle y \\) do not have the same measure

Explanation:

Step1: Check the length of \(CD\) and \(YZ\)

Coordinates of \(C(-2,2)\) and \(D(-7,2)\). Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), for \(CD\), \(y_1 = y_2=2\), so \(d_{CD}=\vert-2-(-7)\vert = 5\).
Coordinates of \(Y(7,-3)\) and \(Z(3,-3)\). For \(YZ\), \(y_1 = y_2=-3\), so \(d_{YZ}=\vert7 - 3\vert=4\).
Since \(CD = 5\) and \(YZ=4\), \(CD
eq YZ\).

Step2: Analyze congruence condition

For two quadrilaterals to be congruent, all corresponding sides and angles must be equal. Since \(CD\) and \(YZ\) (corresponding sides) are not equal, the quadrilaterals are not congruent.

Answer:

No, because \(\overline{CD}\) and \(\overline{YZ}\) do not have the same length.