Question

Find the coordinates of the orthocentre of the triangle whose vertices are $A(0,0),B(-2,5),(4,3)$

Answer 1

Slope of line perpendicular to $BC$ is $3$

Equation of altitude from $A$

$y=3x$.............(i)

$m_{AC}=\frac{3}{4}$

Equation altitude from $B$:

$\begin{array}{c}y-5=-\frac{4}{3}\left(x+2\right)\\ 3y-15=-4x-8\\ 3y+4x=\mathrm{7........}\left(ii\right)\end{array}$

From $\left(i\right)$ & $\left(ii\right)$

$\left(\frac{7}{13},\frac{21}{13}\right)$=Coordinates of orthocentre of triangle.