Question

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

Answer 1

Given three vertices of a triangle $(-5,-1)(3,-5)(5,2)$ the area is given by the formula

$=\left|\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]\right|$

$=\left|\frac{1}{2}[-5(-5-2)+3(2+1)+5(-1+5)]\right|$

$=\left|\frac{1}{2}[+35+9+20]\right|$

$=\left|\frac{1}{2}[29+35]\right|$

$=\frac{64}{2}$

$=32$ sq units.