Question

The orthocentre of the triangle with vertices $(2,\frac{\sqrt{3}-1}{2}),(\frac{1}{2},\frac{-1}{2})$ and $(2,-\frac{1}{2})$ is

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

Answer 1

Answer: (B)

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

Let $A=(2,\frac{\sqrt{3}-1}{2})$

$B=(\frac{1}{2},-\frac{1}{2})$

$C=(2,-\frac{1}{2})$

Clearly the given points form a right angles triangle, right angled at $C$ .

Clearly the given points form a right angled triangle, rightangled at $C$.

$\Rightarrow$ Orthocentre= $C=(2,-\frac{1}{2})$ .