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

Given,

ΔABC is equilateral triangle base BC lies on Y-axis and coordinates of C are (0,–3).

As the base lies on y-axis which implies coordinates of B would be (0, y) because x coordinate will be zero.

Also, origin is midpoint i.e. (0,0)

The midpoint of the line segment joining the points and is .

∴ For coordinates of B

⇒

∴ coordinates of B(0,3)

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

AB = BC ⇒ AB² = BC²

⇒ (x–0)² + (0–3)² = 6²

⇒ x² = 36–9 = 27

⇒

If the coordinates of point A are (,0) then the coordinates of D are (.

If the coordinates of point A are (,0) then coordinates of D are (.