Question

The base BC of an equilateral triangle ABC lies on y-axis. The coordinates of point C are (0, -3). The origin is the midpoint of the base. Find the coordinates of the points A and B. Also, find the coordinates of another point D such that ABCD is a rhombus.

Answer 1

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

0 = -3+y/2

y = 3

Thus, the coordinates of B are (0, 3)

Here. AB = BC = AC and by symmetry the coordinates of A lies on x-axis Let the coordinates of A be (x, 0). Then