First slide

Cartesian plane

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

Moderate

A

$(\frac{3}{2}, \frac{\sqrt{3} - 3}{6})$
B

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

$(\frac{5}{4}, \frac{(\sqrt{3} - 2)}{4})$
D

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

Solution

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

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