Question

Prove that area if triangle $ABC$ with vertices $A(3,2),B(11,8),C(8,12)$ is $25$ square units.

Answer 1

Given that,

$A=(3,2)$

$B=(11,8)$

$C=(8,12)$

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

$=\frac{1}{2}|3(8-12)+11(12-2)+8(2-8)|$

$=\frac{1}{2}|3(-4)+11\left(10\right)+8(-6)|$

$=\frac{1}{2}|-12+110-48|$

$=\frac{1}{2}\left(50\right)$

$=25$ Sq.units