Question

Lines AB and CD having the following points: A(2,4) B(9,8) C(-1,2) and D(3,-5). Are the lines parallel, perpendicular, or neither

Answer 1

perpendicular

Explanation:

Calculate the slopes m of AB and CD using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = A(2, 4) and (x₂, y₂ ) = B(9, 8)

m =
`(8-4)/(9-2)` =
`(4)/(7)`

Repeat with

(x₁, y₁ ) = C(- 1, 2) and (x₂, y₂ ) = D(3, - 5)

m =
`(-5-2)/(3+1)` = -
`(7)/(4)`

The slopes are not equal, hence AB and CD are not parallel

The slope are negative inverses of each other, hence

AB and CD are perpendicular