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, a1​x+b1​y=c1​ and a2​x+b2​y=c2​, are perpendicular if a1​a2​+b1​b2​=0. In (1) a1​=−2. b1​=3 and in (4) a2​=3.b2​=2, so that a1​a2​+b1​b2​=−6+6=0.