Question

Given A(-4-5), B(8,-1), C (-5, 9), and D (2,8) determine whether AB is parallel,

perpendicular, or neither to CD

Answer 1

neither

Explanation:

If 2 lines are parallel then their slopes are equal

If 2 lines are perpendicular then the product of their slopes = - 1

Calculate the slopes m using the slope formula

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

with (x₁, y₁ ) = A (- 4, - 5 ) and (x₂, y₂ ) = B (8, - 1 )

`m_(AB)` =
`(-1-(-5))/(8-(-4))` =
`(-1+5)/(8+4)` =
`(4)/(12)` =
`(1)/(3)`

Repeat

with (x₁, y₁ ) = C (- 5, 9 ) and (x₂, y₂ ) = D (2, 8 )

`m_(CD)` =
`(8-9)/(2-(-5))` =
`(-1)/(2+5)` = -
`(1)/(7)`

The slopes are neither equal nor have a product of - 1