Question

Find the coordinates of the orthocentre of triangles when vertices are $(2,0),(3,4)$ and $(0,3)$

Answer 1

Let the orthocentre be $(h,k)$ then;

$\frac{k-3}{h-0}\frac{4-0}{3-2}=-1$

$⟹h=-4(k-3)$

$\frac{k-0}{h-2}\frac{4-3}{3-0}=-1$

$⟹k=6-3h$

$⟹h=\frac{12}{11},k=\frac{30}{11}$