Question

determine whether any of the lines in the figure are parallel or perpendicular.
select choice
part b
justify your answer.
\\( \overleftrightarrow { p q } \\) select choke \\( \overleftrightarrow { t u } \\) because select choice a slope of \\( - \frac { 2 } { 3 } \\).

Explanation:

Step1: Find the slope of line \(PQ\)

Use the slope formula \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let \(P(-1,3)\) and \(Q(5,1)\). Then \(m_{PQ}=\frac{1 - 3}{5+1}=\frac{-2}{6}=-\frac{1}{3}\)

Step2: Find the slope of line \(TU\)

Let \(T(-3,-1)\) and \(U(0,-2)\). Then \(m_{TU}=\frac{-2 + 1}{0+3}=\frac{-1}{3}=-\frac{1}{3}\)

Step3: Find the slope of line \(RS\)

Let \(R(-2,1)\) and \(S(3,0)\). Then \(m_{RS}=\frac{0 - 1}{3+2}=-\frac{1}{5}\)

Step4: Check parallel and perpendicular

Since \(m_{PQ}=m_{TU}=-\frac{1}{3}\), lines \(PQ\) and \(TU\) are parallel.

Answer:

Lines \(PQ\) and \(TU\) are parallel.