Problem: Given the four equations: (1) 3y−2x=12, (2) −2x−3y=10, (3) 3y+2x=12, (4) 2y+3x=10. The pair representing perpendicular lines is:
Answer Choices:
A. (1) and (4)
B. (1) and (3)
C. (1) and (2)
D. (2) and (4)
E. (2) and (3)
Solution:
Two lines are perpendicular when the product of their slopes is −1 . Since the slopes are, respectively, 32,−32,−32,−23, and, since (32)(−23)=−1. lines (1) and (4) are perpendicular.
or
Two lines, a1x+b1y=c1 and a2x+b2y=c2, are perpendicular if a1a2+b1b2=0. In (1) a1=−2. b1=3 and in (4) a2=3.b2=2, so that a1a2+b1b2=−6+6=0.