Question

Write the coordinates of the orthocentre of the triangle formed by points (8, 0), (4, 6) and (0, 0).

Answer 1

The intersection point of three altitudes of a triangle is called orthocentre.

In the figure, two altitudes ON and BM of $∆$OAB are shown.

Slope of AB = $\frac{6-0}{4-8}=-\frac{3}{2}$

$\therefore$ Slope of ON $=\frac{2}{3}\left(\because \mathrm{Product}\mathrm{of}\mathrm{slopes}=-1\right)$
Equation of ON:

$$\begin{gathered} \left(y-0\right)=\frac{2}{3}\left(x-0\right) \\ y=\frac{2}{3}x \end{gathered}$$ ... (1)

Equation of BM:

x = 4 ... (2)

On solving equations (1) and (2), we get $\left(4,\frac{8}{3}\right)$ as the coordinates of the orthocentre.