Question

The base QR of a n equilateral triangle PQR lies on x-axis. The coordinates of the point Q are (-4, 0) and origin is the midpoint of the base. Find the coordinates of the points P and R.

Answer 1

Let (x,0) be the coordinates of R. Then

\(0=\frac{-4\,+\,x}{2}\) \(\Rightarrow x=4\)

Thus, the coordinates of R are (4,0).

Here, PQ = QR = PR and the coordinates of P lies on y-axis.

Let the coordinates of P be (0,y). Then,

Hence, the required coordinates are R(4,0) and P(\(0,4\sqrt{3}\)) or P(\(0,-4\sqrt{3}\)).