Question

lines mn and pq are parallel. lines rs and tv intersect them. which statements are true about these lines? select three options. the slope of line mn is \\(\frac{2}{3}\\). the slope of line pq is undefined. the slope of line rs is \\(-\frac{3}{2}\\). lines rs and tv are parallel. line rs is perpendicular to both line mn and line pq.

Explanation:

Step1: Analyze slope of MN

Points on MN: M(-3, -1), N(3, 3). Slope formula: $m=\frac{y_2 - y_1}{x_2 - x_1}$. So $m_{MN}=\frac{3 - (-1)}{3 - (-3)}=\frac{4}{6}=\frac{2}{3}$. Correct.

Step2: Analyze slope of PQ

PQ is parallel to MN, so same slope as MN ($\frac{2}{3}$), not undefined. Incorrect.

Step3: Analyze slope of RS

Points on RS: R(-2, 4), S(2, -2). Slope: $m_{RS}=\frac{-2 - 4}{2 - (-2)}=\frac{-6}{4}=-\frac{3}{2}$. Correct.

Step4: Analyze RS and TV parallel

TV: points T(-4, 1), V(0, -4). Slope: $m_{TV}=\frac{-4 - 1}{0 - (-4)}=\frac{-5}{4}
eq-\frac{3}{2}$. Not parallel. Incorrect.

Step5: Analyze RS perpendicular to MN/PQ

Product of slopes: $m_{MN}\times m_{RS}=\frac{2}{3}\times(-\frac{3}{2})=-1$. So perpendicular. Correct.

Answer:

• The slope of line MN is $\frac{2}{3}$.
• The slope of line RS is $-\frac{3}{2}$.
• Line RS is perpendicular to both line MN and line PQ.