Lines AB and CD are neither parallel nor perpendicular.
How to determine perpendicularity of lines
To determine whether the line segments AB and CD are parallel, perpendicular, or neither, we can compare their slopes.
The slope m of a line passing through points (x₁, y₁) and (x₂, y₂) is given by:
m = (y₂ - y₁)/(x₂ - x₁)
For AB, the slope is:
m₁ = (3 - 0)/(5 - 1
= 3/4
For CD, the slope is:
m₂ = (2 - (-1))/(0 - 6)
= 3/6
= 1/2
Now, compare the slopes:
For two lines to be perpendicular,
m₁*m₂ = -1
But
m₁*m₂ = 3/4*1/2 = 3/8
m₁*m₂ ≠ -1 Not perpendicular
For two lines to be parallel,
m₁ = m₂
But
m₁ ≠ m₂ Not parallel
Therefore, AB and CD are neither parallel nor perpendicular.
Complete question
Use the slopes of AB and CD to determine whether AB and CD are parallel, perpendicular, or neither.
A(1, 0) B(5, 3)
C(6, -1) D(0, 2)