Question

select whether the pair of lines is parallel, perpendicular, or neither.

Explanation:

Step1: Find slope of line AB

Let \(A=(x_1,y_1)\) and \(B=(x_2,y_2)\). Assume \(A = (- 4,3)\) and \(B=(4,1)\). The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Then \(m_{AB}=\frac{1 - 3}{4-(-4)}=\frac{-2}{8}=-\frac{1}{4}\).

Step2: Find slope of line CD

Let \(C=(x_3,y_3)\) and \(D=(x_4,y_4)\). Assume \(C=(0,2)\) and \(D = (-2,-2)\). Then \(m_{CD}=\frac{-2 - 2}{-2-0}=\frac{-4}{-2}=2\).

Step3: Check relationship

Two lines are parallel if their slopes are equal (\(m_1 = m_2\)), and perpendicular if \(m_1\times m_2=- 1\). Here, \(-\frac{1}{4}
eq2\) and \(-\frac{1}{4}\times2=-\frac{1}{2}
eq - 1\).

Answer:

Neither