# How do you find the area of a triangle plot as point A = (-2,5); B = (12,3); C = (10,-11)?

Jul 9, 2015

I found $100$ units of area

#### Explanation:

There may be different ways to solve this but I thought of one that is quite intriguing:
Area=$\pm \frac{1}{2} | \left({x}_{1} , {y}_{1} , 1\right) , \left({x}_{2} , {y}_{2} , 1\right) , \left({x}_{3} , {y}_{3} , 1\right) |$
i.e. $\frac{1}{2}$ times the determinant formed using your coordinates and a column of $1$ (the $\pm$ is to "correct" possible negative values).
Area=$\pm \frac{1}{2} | \left(- 2 , 5 , 1\right) , \left(12 , 3 , 1\right) , \left(10 , - 11 , 1\right) | = \pm \frac{1}{2} \left(- 200\right) = 100$ u.a.