Question

The base BC of an equilateral triangle ABC lies on y- axis . The coordinates of the point C are (0,-3). If the origin is the mid-point of the base BC, find the coordinates of the points A and B.

Answer 1

O is the mid-point of the base BC.

Therefore, coordinates of point B are (0,3).

So, BC = 6 units

Let the coordinates of point A be (x,0).

Using distance formula,

$AB=\sqrt{(0-x{)}^2+(3-0{)}^2}=\sqrt{x^2+9}$

$BC=\sqrt{(0-0{)}^2+(-3-3{)}^2}=\sqrt{36}$

Also, AB = BC

$\sqrt{x^2+9}=\sqrt{36}$

$x^2+9=36$

$x^2=27$

$x=\pm 3\sqrt{3}$

Coordinates of A = $(3\sqrt{3},0)$.