Question

The orthocenter 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. $(0,0)$
• D. $(\frac{1}{4},\frac{1}{4})$

Answer 1

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

The lines by which triangle is formed are $x=0,y=0andx+y=1.$ Clearly, it is a right triangle. We know that in a right - angled triangle, the orthocenter coincides with the vertex at which right angle is formed. Therefore, the orthocenter is (0,0).