Problem:
Line has equation and goes through . Line has equation and meets line at point . Line has positive slope, goes through point , and meets at point . The area of is 3 . What is the slope of ?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The solution to the system of equations and is . The perpendicular distance from to is 3 . The area of is , so . Thus point is 2 units to the right or to the left of . If then the line is vertical and the slope is undefined. If , then the line has slope .
The problems on this page are the property of the MAA's American Mathematics Competitions