Question

Write the coordinates of the orthocentre of the triangle whose vertices are at $(0,0),(6,0)$ and $(0,10)$.

Answer 1

So, we have right angled triangle.

Now the orthocenter is the point of intersection of the altitudes. Each leg in a right angle triangled form an altitude. So in a right angled triangle, the orthocenter lies at the vertex containing the right angle.

So, the orthocenter of the triangle with vertices $(0,0)(6,0)$ and $4(0,10)$

is simply $(0,0)$.