Question

determine whether any of the lines in the figure are parallel or perpendicular.
select choice
part b

Explanation:

Step1: Find slopes of lines

Use the slope formula \(m = \frac{y_2 - y_1}{x_2 - x_1}\).
For line \(PQ\): Let \(P(-2, 3)\) and \(Q(4, 0)\), then \(m_{PQ}=\frac{0 - 3}{4-(-2)}=-\frac{1}{2}\).
For line \(RS\): Let \(R(-3, 1)\) and \(S(3,-1)\), then \(m_{RS}=\frac{-1 - 1}{3-(-3)}=-\frac{1}{2}\).
For line \(TU\): Let \(T(-3,-1)\) and \(U(0,-3)\), then \(m_{TU}=\frac{-3-(-1)}{0 - (-3)}=-\frac{2}{3}\).

Step2: Check parallel and perpendicular

Parallel lines have equal slopes. Since \(m_{PQ}=m_{RS}=-\frac{1}{2}\), lines \(PQ\) and \(RS\) are parallel.
Perpendicular lines have slopes \(m_1\times m_2=-1\). Here, no pair of slopes ( \(m_{PQ}\times m_{TU}=(-\frac{1}{2})\times(-\frac{2}{3})=\frac{1}{3}
eq - 1\), \(m_{RS}\times m_{TU}=(-\frac{1}{2})\times(-\frac{2}{3})=\frac{1}{3}
eq - 1\)) satisfy the perpendicular condition.

Answer:

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