Question

Find the areas of the triangles the whose coordinates of the points are respectively.

(5, 2), (-9, -3) and (-3, -5)

Answer 1

Area of triangle having angular points
$(x_1,y_1),$ $(x_2,y_2)$ and $(x_3,y_3)$ is given by the formula
$△=\frac{1}{2}|x_1{y}_2+x_2{y}_3+x_3{y}_1-x_2{y}_1-x_3{y}_2-x_1{y}_3|$
$△=\frac{1}{2}|5\times -3+-9\times -5+-3\times 2-(-9)\times 2-(-3)\times (-3)-5\times (-5\left)\right|$
$\Rightarrow △=\frac{1}{2}|-15+45-6+18-9+25|$
$\Rightarrow △=\frac{1}{2}\times 58=29$