Question

find the area of the triangle whose are (-5,-1) (3,-5) (5,2).

Answer 1

Points: $(-5,-1)(,-5)(5,2)$

$x_1=5,y_1=-1,x_2=3,y_2=-5,x_3=5,y_3=2$

Area of the triangle

$=\frac{1}{2}\left[x,(y_2-y_3)+x_2(y_3-y_{1)})+x_3(y_1-y)\right]$

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

$=\frac{1}{2}\left[-5(-7)+3\left(3\right)+5(-1+5)\right]$

$=\frac{1}{2}\left[35+9+5+\left(4\right)\right]$

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

$=\frac{1}{2}\left[35+29\right]\Rightarrow \frac{1}{2}\left[64\right]$

$=32$

The area of triangle is = $32$