Question

1. - determine whether \\( \overleftrightarrow { a b } \\) and \\( \overleftrightarrow { c d } \\) are parallel, perpendicular, or neither

graph each line to verify your answer. justify your answer.
\\( a ( 4, - 2 ), b ( - 2, - 8 ), c ( 4, 6 ), d ( 8, 5 ) \\)

Explanation:

Step1: Calculate the slope of \(\overleftrightarrow{AB}\)

The slope formula is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For points \(A(4,-2)\) and \(B(-2,-8)\), \(m_{AB}=\frac{-8-(-2)}{-2 - 4}=\frac{-8 + 2}{-6}=\frac{-6}{-6}=1\)

Step2: Calculate the slope of \(\overleftrightarrow{CD}\)

For points \(C(4,6)\) and \(D(8,5)\), \(m_{CD}=\frac{5 - 6}{8 - 4}=\frac{-1}{4}=-\frac{1}{4}\)

Step3: Check the relationship between slopes

Two lines are parallel if \(m_1=m_2\). Here \(1
eq-\frac{1}{4}\). Two lines are perpendicular if \(m_1\times m_2=-1\). \(1\times(-\frac{1}{4})=-\frac{1}{4}
eq - 1\)

Answer:

\(\overleftrightarrow{AB}\) and \(\overleftrightarrow{CD}\) are neither parallel nor perpendicular.