Question

Find the sum of coordinates of the orthocentre of the triangle whose sides are $x=3,y=4$ and $3x+4y=6$.

• A. $(0,0)$
• B. $(3,0)$
• C. $(0,4)$
• D. $(3,4)$

Answer 1

The correct option is D $(3,4)$

As we can see that the triangle formed by the given lines is a right angled triangle. The orthocenter is the point where all three altitude of the triangle intersect. Hence, in a right triangle, the vertex of the right angle is where you would expect the altitudes to meet, at $90$ degrees, where the legs of the right triangle are perpendicular. Therefore, the coordinates of orthocenter are $(3,4)$.