Answer:
They are perpendicular lines AB ⊥ CD ,
because the multiplying of their slopes = -1
Step-by-step explanation:
The rest of the question is the attached figure.
At first you should know that:
The slope of the line ⇒ [tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
The slope of the line AB:
The coordinates of A= (0,-1) and B= (5,3)
∴ The slope of the line AB= m₁ [tex]=\frac{3-(-1)}{5-0}=\frac{4}{5}[/tex]
The slope of the line CD:
The coordinates of C = (2,3) and D = (6,-2)
∴ The slope of the line CD= m₂ = [tex]\frac{-2-3}{6-2}=-\frac{5}{4}[/tex]
Multiplying m₁ and m₂ = [tex]\frac{4}{5}* -\frac{5}{4}=-1[/tex]
By definition, the multiplying of slopes of perpendicular lines = -1
So, The lines are perpendicular because the multiplying of their slopes = -1
