Question

Determine whether AB and CD are parallel, perpendicular,

or neither.
A (12,3), B(-3,9), C (-6,4), D (-2,-6)

Answer 1

Explanation:

we can find the equations for both lines and analyze after

`y = mx + b\\where\\m = (y_2-y_1)/(x_2-x_1)\\\\`

AB:

`(12, 3), (-3, 9)\\m = (9-3)/(-3-12) = (6)/(-15) = (-2)/(5)`

`y = (-2)/(5)(x) + b\\3= (-2(12))/(5) + b\\3 = (-24)/(5) + b\\b = (39)/(5) \\y = (-2)/(5)(x) + (39)/(5)`

CD:

`(-6, 4) (-2, -6)\\m = (4-(-6))/(-6-(-2)) = (10)/(-4) = (-5)/(2) \\y = (-5)/(2)(x) + b\\4 = (-5(-6))/(2) + b\\4 = 15 + b\\b = -11\\y = (-5)/(2)(x) - 11`

Determining whether two lines are parallel or perpendicular involves looking at their slopes. AB has a slope of -2/5, CD has a slope of -5/2. Since these are not equal (not parallel) and not negative reciprocals of each other (not perpendicular), the lines are neither perpendicular or parallel.