Problem: A triangle is formed by joining three points whose coordinates are integers. If the -unit and the -unit are each inch, then the area of the triangle, in square inches, must be an integer
Answer Choices:
A. must be an integer
B. may be irrational
C. must be irrational
D. must be rational
E. will be an integer only if the triangle is equilateral.
Solution:
There is no loss of generality by placing one vertex at the origin, . Let the other two vertices be and . Let and be the projections of and , respectively, on the -axis.
This may be integral or fractional