1958 AHSME Problem 35

A triangle is formed by joining three points whose coordinates are integers. If the x-coordinate and the y-coordinate each have a value of 1, then the area of the triangle, in square units:

\begin{array}{l} \textbf{(A)}\ \text{must be an integer}\qquad \textbf{(B)}\ \text{may be irrational}\qquad \textbf{(C)}\ \text{must be irrational}\qquad \textbf{(D)}\ \text{must be rational}\qquad \\ \textbf{(E)}\ \text{will be an integer only if the triangle is equilateral.} \end{array}

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.