Question

The orthocentre of the triangle with vertices

$\left( 2,\frac{\sqrt{3} - 1}{2} \right)$, $\left( \frac{1}{2}, - \frac{1}{2} \right)$ and $\left( 2, - \frac{1}{2} \right)$ is.

• A. $\left( \frac{3}{2},\frac{\sqrt{3} - 3}{6} \right)$
• B. $\left( 2, - \frac{1}{2} \right)$
• C. $\left( \frac{5}{4},\frac{\sqrt{3} - 2}{4} \right)$
• D. $\left( \frac{1}{2}, - \frac{1}{2} \right)$

Answer 1

Answer: (B)

$\left( 2, - \frac{1}{2} \right)$

Answer 2

Here, the given triangle is a right angled triangle at the vertex $\left( 2 , - \frac { 1 } { 2 } \right)$ . Hence the orthocentre is at $\left( 2 , \frac { - 1 } { 2 } \right)$.