Two points on L1 and two points on L2 are given. Determine whether L1 is parallel to L2, L1 is perpendicular to L2, or
neither.
-L1: (1, -3), (2, -7); L2: (3, 3), (7, 4)
A) parallel
B) perpendicular
C) neither

Question

Quizplus · Accepted Answer

First, we need to find the slopes of both lines:

slope of L1 = (change in y)/(change in x) = (-7 - (-3))/(2 - 1) = -4/1 = -4
slope of L2 = (4 - 3)/(7 - 3) = 1/4

Since the slopes are not equal (i.e. -4 ≠ 1/4), the lines are not parallel.

If two lines are perpendicular, then their slopes are negative reciprocals of each other. That is, if m1 and m2 are the slopes, then m1 x m2 = -1. Let's see:

-4 x (1/4) = -1

So, the two lines are perpendicular, and the answer is B.

Two Points on L1 and Two Points on L2 Are