Question

Find the area of the triangle whose vertices are $(-5,-1)(3,-5)(5,2).$

Answer 1

$A(-5,-1)B(3,-5)C(5,2)$

Area of $△ABC=\frac{1}{2}$ $$\left|\begin{array}{ccc}-5& -1& 1\\ 3& -5& 2\\ 5& 2& 1\end{array}\right|$$

$=\frac{1}{2}|-5(-7)+1(-2)+1\left(31\right)|$

$=\frac{1}{2}|35-2+31|$

$=\frac{1}{2}\times 64=32squnits$.