Question

If the area of triangle formed by points $A(x,y),B(1,2)$ and $C(2,1)$ is $68$ units then show that $x+y=15$.

Answer 1

Let the given point is $A(x,y),B(1,2),C(2,1)$

Area of a triangle ABC $=\frac{1}{2}\left[x_1\right(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2\left)\right]$

$6=\frac{1}{2}\left[x\right(2-1)+1(1-y)+2(y-2\left)\right]$

on solving

$x+y=15$