Question

Find the coordinates of the orthocentre of the triangle formed by the line $2x-y-9=0,x-2y+9=0$ and $x+y-9=0$

Answer 1

Given equation are

$2x-y-9=0......\left(1\right)$

$x-2y+9=0......\left(2\right)$

$x+y-9=0......\left(3\right)$

On soving (1), (2) and (3) to, and we get,

$(x_1,y_1)=(9,9)$

$(x_2,y_2)=(3,6)$

$(x_3,y_3)=(6,3)$

Orthocentre is

$\Rightarrow (\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

$\Rightarrow (\frac{9+3+6}{3},\frac{9+6+3}{3})$

$\Rightarrow (\frac{18}{3},\frac{18}{3})$

$\Rightarrow (6,6)$

Hence this is the answer.