Question

The orthocentre of the triangle formed by the lines $xy=0$ and $x+y=1$ is $(a,b)$. Find $a+b$.

Answer 1

Triangle formed by line

$L_1:x=0$

$L_2:y=0$ and

$L_3:x+y=1$ is right angle triangle ( right angle at origin).

And for a right angle triangle orthocentre lies on the vertex which forms right angle.

So coordinates of orthocentre is $(a,b)=(0,0)$

Sum of coordinates $=a+b=0+0=0$