Problem:
What is the area of the triangle formed by the lines
Answer Choices:
A.
B.
C.
D.
E.
Solution:
First, let us find the vertices of the triangles. The intersections between and the other two lines are and . To find the third intersection, we can equate the two equations to get: . This gives us the point .
Note that the first two intersection points are mirrored across the -axis. This tells us that the triangle is isosceles. The base is therefore , and the height is . The area of the triangle is therefore .
Thus, the correct answer is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions