Question

An equilateral triangle has its centroid at origin and one side is x + y = 1. The equations of the others sides are

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Third vertex ‘A’ lies on x – y =0 and in III quadrent
Perpendicular distance from (0,0) to x + y =1 is $\frac{1}{\sqrt{2}}$
\(\therefore AO = \sqrt{2} \Rightarrow A(-1,-1)\)
If m is the slope of other side,
\(\tan 60^\circ = \left | \frac{m+1}{1-m} \right |\)
$\Rightarrow m=2\pm \sqrt{3}$