Question

the graph shows triangles pqr and vwx. is pqr congruent to vwx? justify your answer. yes, because a rotation 90° counterclockwise around r followed by a reflection across the line y = x maps pqr onto vwx. yes, because a rotation 90° clockwise around the origin maps pqr onto vwx. no, because \\( \overline { pq } \\) and \\( \overline { vw } \\) do not have the same length. no, because \\( \angle p \\) and \\( \angle v \\) do not have the same measure.

Explanation:

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

Use the distance formula \( d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2} \). Let \( P(1,3) \) and \( Q(5,-2) \).
\( d_{PQ}=\sqrt{(5 - 1)^2+(-2 - 3)^2}=\sqrt{16 + 25}=\sqrt{41} \)

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

Let \( V(3,-1) \) and \( W(-2,-6) \).
\( d_{VW}=\sqrt{(-2 - 3)^2+(-6+1)^2}=\sqrt{25 + 25}=\sqrt{50} \)

Answer:

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