Question

Determine whether line AB and line CD are parallel, perpendicular, or neither. A( 4, 2), B(-3, 1), C(6, 0), D(-10, 8)

Answer 1

Answer:

neither

Step-by-step explanation:

If AB an CD are parallel, then their slopes are the same.

If AB and CD are perpendicular, then the product of their slopes is equal -1.

The formula of a slope:

$m=\dfrac{y_2-y_1}{x_2-x_1}$

Calculate the both slope:

$A(4,\ 2),\ B(-3,\ 1)\\\\m_{AB}=\dfrac{1-2}{-3-4}=\dfrac{-1}{-7}=\dfrac{1}{7}\\\\C(6,\ 0),\ D(-10,\ 8)\\\\m_{CD}=\dfrac{8-0}{-10-6}=\dfrac{8}{-16}=-\dfrac{1}{2}\\\\=============================$

$m_{AB}\neq m_{CD}$

The line AB and line CD are not parallel

$m_{AB}\cdot m_{CD}=\left(\dfrac{1}{7}\right)\left(-\dfrac{1}{2}\right)=-\dfrac{1}{14}\neq-1$

The line AB and line CD are not perpendicular.