Let A, B and C be \(\left(2, \frac {\sqrt 3 - 1}2\right), \left(\frac 12, - \frac 12\right)\) and \((2, -\frac 12)\)
\({D_{AB}}^2 = (2 - \frac 12)^2+ \left(\frac {\sqrt 3 - 1}2 + \frac 12\right)^2\)
\({D_{AB}}^2 = 3\)
\({D_{BC}}^2 = (\frac 12 - 2)^2 + (-\frac12 +\frac 12)^2\)
\({D_{AC}}^2 = \frac 34\)
Looking closely, we see that
BC2 + AC2 = AB2
The points \(\left(2, \frac{\sqrt 3 - 1}2\right), \left(\frac 12, - \frac 12\right)\) and \(\left(2, -\frac 12\right)\) are the vertices of a right triangle.
Since \(\left(2, -\frac 12\right)\) is the vertex where the right angle is formed.
∴Orthocentre is \(\left(2, -\frac 12\right)\).
