Problem:
Distinct points , and lie on a line, with . Points and lie on a second line, parallel to the first, with . A triangle with positive area has three of the six points as its vertices. How many possible values are there for the area of the triangle?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
The base of the triangle can be , or , and its altitude is the distance between the two parallel lines, so there are possible values for the area.
The problems on this page are the property of the MAA's American Mathematics Competitions