What is the area of △ABC?

Question

The vertices of △ABC are A(0, 8), B(12, 3), and C(7, –9). What is the area of △ABC?

Answer 1

There are 2 ways to do this.

Calculate the length of each side using the distance formula and then use Heron's formula.

Or

Evaluate the determinant which is not easy to write in this editor : a_1k = x_k, a_2k=y_k and a_3k=1 for k=1 to 3.

Either way gives you a lot of arithmetic to do.

If you have further questions, please let me know.