Question

question 4: are \\( \overleftrightarrow { a b } \\) and \\( \overleftrightarrow { c d } \\) parallel, perpendicular, or neither? \\( a ( - 4 : 4 ) b ( - 6 : 6 ) c ( 10, - 8 ), d ( - 2,8 ) \\)

Explanation:

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

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

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

For points \(C(10,-8)\) and \(D(-2,8)\), \(m_{CD}=\frac{8-(-8)}{-2 - 10}=\frac{16}{-12}=-\frac{4}{3}\)

Step3: Check the relationship

Since \(m_{AB}
eq m_{CD}\) (so not parallel) and \(m_{AB}\times m_{CD}=(-1)\times(-\frac{4}{3})=\frac{4}{3}
eq - 1\) (so not perpendicular)

Answer:

Neither