Question

The orthocentre of the triangle formed by the lines $xy=0$ and $x+y=1$ is :

• A. $(\frac{1}{2},\frac{1}{2})$
• B. $(\frac{1}{3},\frac{1}{3})$
• C. $(\frac{1}{4},\frac{1}{4})$
• D. $(0,0)$

Answer 1

The correct option is D $(0,0)$

Given equation of lines are,

$xy=0\to x=0andy=0x+y=1$

the figure of the triangle formed by the given lines

In right angle triangle The orthocenter lies exactly at that vertex at which angle is $90$

$\therefore$ Orthocenter is (0,0)