Question

On the line segment joining the points (1 , 0) and (2 , 0) an equilateral triangle is constructed whose vertex lies in the positive quadrant . Find the third vertex.

Answer 1

The given side of length 1 lies along x-axis and the third vertex will lie on a line perpendicular to x-axis and passing through mid-point (3/2, 0) of given side. Let it be (3/2, k), then
k = CD = 1 . sin ${60}^{\circ }=\frac{\sqrt{3}}{2}$
$\therefore A(1,0)B(2,0),C(3/2,\sqrt{3}/2)$