Question

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

Answer 1

Answer:

AB and CD are parallel lines

Step-by-step 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 = $\frac{8-4}{3-1}$ = $\frac{4}{2}$ = 2

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

m = $\frac{14-6}{3+1}$ = $\frac{8}{4}$ = 2

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

Answer 2

Answer: Parallel

Step-by-step explanation:

$slope (m)= \dfrac{y_2-y_1}{x_2-x_1}$

$m_{AB}=\dfrac{8-4}{3-1}=\dfrac{4}{2}=2$

$m_{CD}=\dfrac{14-6}{3+1}=\dfrac{8}{4}=2$

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