Question

Which statement best explains the relationship between lines CD and FG?

A:They are perpendicular because their slopes are equal.
B:They are perpendicular because their slopes are negative reciprocals.
C:They are not perpendicular because their slopes are equal.
D:They are not perpendicular because their slopes are negative reciprocals.

Answer 1

b. they perpendicular because their slopes are negative reciprocals

Explanation:

Answer 2

B

calculate the slopes m of the 2 lines using the gradient formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = C(- 2, 4) and (x₂, y₂ ) = D(0, - 4 )

`m_(CD)` =
`(-4-4)/(0+2)` =
`(-8)/(2)` = - 4

repeat with (x₁, y₁ ) = F(- 4, 0 ) and (x₂, y₂ ) = G(4, 2 )

`m_(GF)` =
`(2-0)/(4+4)` =
`(2)/(8)` =
`(1)/(4)`

The 2 lines are perpendicular because their slopes are negative reciprocals