Question

Given the points A(0, 0), B(e, f), C(0, e) and D(f, 0), determine if line segments AB and CD are parallel, perpendicular or neither.

Answer 1

Perpendicular

Explanation:

Calculate the slopes m of the segments using the slope formula.

m =
`(y_(2)-y_(1) )/(x_(2)-x_(1) )`

Parallel lines have equal slopes

The product of the slopes of perpendicular lines equals - 1

(x₁, y₁ ) = A(0, 0) and (x₂, y₂ ) = B(e, f)

`m_(AB)` =
`(f-0)/(e-0)` =
`(f)/(e)`

Repeat with (x₁, y₁ ) = C(0, e) and (x₂, y₂ ) = D(f, 0)

`m_(CD)` =
`(0-e)/(f-0)` = -
`(e)/(f)`

Thus AB and CD are perpendicular since
`(f)/(e)` × -
`(e)/(f)` = - 1