Question

$overline{pq}$ is parallel to $overline{xy}$. what is the length of $overline{rx}$ in centimeters? the options are 4, 6, 3, 2.

Explanation:

\). Given \( PQ = 4 \), \( QR = 6 \), \( YR = 4 \), \( PR = 8 \). So \( \frac{PQ}{XY} = \frac{6}{4} = \frac{3}{2} \). Therefore, \( \frac{PR}{XR} = \frac{3}{2} \), so \( \frac{8}{XR} = \frac{3}{2} \) → \( XR = \frac{16}{3} ≈ 5.33 \), not an option. Wait, maybe the triangles are \( \triangle PQR \) and \( \triangle XYR \), but the ratio is \( \frac{PQ}{XY} = \frac{PR}{XR} \), and \( PQ = 4 \), \( XY = 4 \), so \( \frac{4}{4} = \frac{8}{XR} \) → \( XR = 8 \), not an option. Wait, the options are 4,6,3,2. Maybe the correct answer is 6? No, 6 is the length of \( QR \

Answer:

\). Given \( PQ = 4 \), \( QR = 6 \), \( YR = 4 \), \( PR = 8 \). So \( \frac{PQ}{XY} = \frac{6}{4} = \frac{3}{2} \). Therefore, \( \frac{PR}{XR} = \frac{3}{2} \), so \( \frac{8}{XR} = \frac{3}{2} \) → \( XR = \frac{16}{3} ≈ 5.33 \), not an option. Wait, maybe the triangles are \( \triangle PQR \) and \( \triangle XYR \), but the ratio is \( \frac{PQ}{XY} = \frac{PR}{XR} \), and \( PQ = 4 \), \( XY = 4 \), so \( \frac{4}{4} = \frac{8}{XR} \) → \( XR = 8 \), not an option. Wait, the options are 4,6,3,2. Maybe the correct answer is 6? No, 6 is the length of \( QR \