Question

Determine if line AB and line CD are parallel, perpendicular, or neither.

A(1,4) B(3,8)

C(-1,6) D(3, 14)

Answer 1

AB and CD are parallel lines

Explanation:

• Parallel lines have equal slopes

• The slopes of perpendicular lines are negative reciprocals

Calculate the slope m using the gradient formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

let (x₁, y₁ ) = A(1, 4) and (x₂, y₂ ) = B(3, 8)

m =
`(8-4)/(3-1)` =
`(4)/(2)` = 2

let (x₁, y₁ ) = C(- 1, 6) and (x₂, y₂ ) = D(3, 14)

m =
`(14-6)/(3+1)` =
`(8)/(4)` = 2

Since slope of AB and CD are equal then lines are parallel

Answer 2

Answer: Parallel

Explanation:

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

`m_(AB)=(8-4)/(3-1)=(4)/(2)=2`

`m_(CD)=(14-6)/(3+1)=(8)/(4)=2`

Since AB and CD have the same slope, they are parallel