Question

the graph shows quadrilaterals hijk and uvwx. is hijk congruent to uvwx? justify your answer. yes, because a reflection across the y - axis maps hijk onto uvwx. yes, because a translation left 10 units and down 2 units maps hijk onto uvwx. no, because \\( \overline { j k } \\) and \\( \overline { w x } \\) do not have the same length. no, because \\( \angle i \\) and \\( \angle v \\) do not have the same measure.

Explanation:

Step1: Calculate the length of \( \overline{JK} \)

Using the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). For \( J(7,7) \) and \( K(5,3) \), \( d_{JK}=\sqrt{(7 - 5)^2+(7 - 3)^2}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5} \).

Step2: Calculate the length of \( \overline{WX} \)

For \( W(-3,5) \) and \( X(-5,2) \), \( d_{WX}=\sqrt{(-3+5)^2+(5 - 2)^2}=\sqrt{4+9}=\sqrt{13} \).
Since \( \sqrt{20}
eq\sqrt{13} \), \( \overline{JK} \) and \( \overline{WX} \) are not equal. Congruent figures have all corresponding sides equal.

Answer:

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