Integral parameter for a triangle with integral area

Question

The area of a triangle formed by the points $(p, 2-2p), (1-p, 2p)$ and $(-4-p, 6-2p)$ is 70. How many integral values of $p$ are possible?

I have been given these options:

1. 2
2. 3
3. 4
4. None of the above

I solved it using the shoelace formula, but is there a better (shorter or easier-to-understand) way than this?

Answer 1

Shift the origin to $(-p,-2p)$.

The vertices of the triangle in the new reference frame become :

$(2p,2)$, $(1,4p)$, and $(-4,6)$.

This will simplify your calculations.