Question

Use the information below to determine if AB and CD are parallel, perpendicular or neither.

(0, – 4), (-1, — 7), (3, 0), (-3, 2)

Answer 1

perpendicular

Explanation:

Calculate the slope:

`m=(y_2-y_1)/(x_2-x_1)`

Let m₁ and m₂ are the slopes of AB and CD.

Then

if m₁ = m₂ → lines are parallel

if m₁ · m₂ = -1 → lines are perpendicular

`A(0;\ -4);\ B(-1;\ -7)\\\\m_(AB)=(-7-(-4))/(-1-0)=(-7+4)/(-1)=(-3)/(-1)=3\\\\C(3;\ 0);\ D(-3;\ 2)\\\\m_(CD)=(2-0)/(-3-3)=(2)/(-6)=-(2:2)/(6:2)=-(1)/(3)`

`m_(AB)\\eq m_(CD)` - no parallel

`m_(AB)\cdot m_(CD)=3\cdot\left(-(1)/(3)\right)=-(3)/(3)=-1` - perpendicular