Question

determine whether any of the lines in the figure are parallel or perpendicular.

justify your answer.

Explanation:

Step1: Find the slope of \(\overleftrightarrow{PQ}\)

Use the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\). Let \(P(-2,3)\) and \(Q(7,0)\). Then \(m_{PQ}=\frac{0 - 3}{7+ 2}=\frac{-3}{9}=-\frac{1}{3}\)

Step2: Find the slope of \(\overleftrightarrow{RS}\)

Let \(R(-3,1)\) and \(S(6,-2)\). Then \(m_{RS}=\frac{-2 - 1}{6 + 3}=\frac{-3}{9}=-\frac{1}{3}\)

Step3: Find the slope of \(\overleftrightarrow{TU}\)

Let \(T(-4,-1)\) and \(U(1,-4)\). Then \(m_{TU}=\frac{-4 + 1}{1+4}=\frac{-3}{5}\)

Since \(m_{PQ}=m_{RS}=-\frac{1}{3}\), \(\overleftrightarrow{PQ}\parallel\overleftrightarrow{RS}\) (parallel lines have equal slopes)

Answer:

\(\overleftrightarrow{PQ}\parallel\overleftrightarrow{RS}\) because they have the same slope of \(-\frac{1}{3}\)