Problem:
The lines with equations and are perpendicular and intersect at . What is ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Because the lines are perpendicular, their slopes, and , are negative reciprocals, so . Substituting for and using the point yields the equations and . Adding the two equations yields , so . Thus .
The problems on this page are the property of the MAA's American Mathematics Competitions