Question

Given a pair of points on each line, use the slope formula to determine whether AB and CD are parallel. perpendicular, or neither. AB: A(-2,-5) and B(4.7) CD: C(0, 2) and D(8,-2)

Answer 1

Perpendicular

Step-by-step explanation:

Given the coordinates

A(-2,-5), B(4.7) C(0, 2) and D(8,-2)​, we are to determine whether AB is parallel, perpendicular to CD or neither

To do this, we need to find he slope of AB and CD first. Using the formula for calculating slope as shown;

m = y2-y1/x2-x1

For AB:

slope = 7-(-5)/4-(-2)

Slope = 7+5/4+2

Slope of AB = 12/6

Slope of AB = 2

For CD

Slope of CD = -2-2/8-0

Slope of CD = -4/8

Slope of CD = -1/2

Note that for AB to be perpendicular to CD, the product of their slope must be -1.

Given

mAB = 2

mCD = -1/2

Taking their product

mAB * mCD = 2 * -1/2

mAB * mCD = -1

Since the product is -1, hence AB is PERPENDICULAR to CD