Question

What is the orthocentre of the triangle formed by the lines $xy=0$, $x+y=0$ is

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

Answer 1

The correct option is C

$\left(0,0\right)$

Explanation for the correct option

Three sides of triangle are

$$\begin{gathered} x=0 \\ y=0 \\ x+y=1 \end{gathered}$$

So, the vertices of the triangle are $O\left(0,0\right),A\left(1,0\right)$ and $B\left(0,1\right)$

Therefore the triangle is a right angle triangle whose vertices is at origin where $90°$angle formed.

So the orthocentre of the triangle is at origin $\left(0,0\right)$.

Hence, option $\left(\mathrm{C}\right)$ is the correct answer.