Skip to main content
OlympiadHQ

Browse · MATH

Print

jmc

algebra intermediate

Problem

Consider the lines Let's say that a pair of lines is if the two lines are either parallel or perpendicular to each other. Among all the pairs of lines shown, how many pairs are good?
Solution
We find the slope for each line. The slopes are , , , , and . Parallel lines have the same slope, therefore lines and are parallel. Perpendicular lines have slopes that are negative reciprocals. None of the slopes above are negative reciprocals, therefore there are no perpendicular lines. There are pairs of lines that are parallel or perpendicular.
Final answer
1