Question

Base AB of an equilateral triangle ABC lies on y – axis. The co-ordinates of A are (0, -2). If origin
is the mid-point of AB, find the co-ordinates of point C.

Answer 1

Step-by-step explanation:

Since, the coordinates of A are (0, -2) and origin is the mid point, coordinates of B must be (0,2).

Now let the coordinates of C be (x,y)

since it's an equilateral triangle,

using distance formula,

$\sqrt{{x}^{2} + {(y - 2)}^{2} } = \sqrt{ { {x}^{2} } + ({y + 2})^{2} } \\ y = 0$

Now, we know AB = 4 units.

using distance formula again, we get,

$\sqrt{ {x}^{2}+ 4 } = 4 \\ {x}^{2} = 12 \\ x = 2 \sqrt{3} \: or \: - 2 \sqrt{3}$

Hope this helps.