if(-4,3)and(4,3)are two vertices of an equilateral triangle. find the coordinates of the third vertex. given that the origin lies in the interior of the triangle.

Let the co-ordinate of third vertex be (*x*, *y*)

Now Using Distance formula

Given, ΔABC is equilateral triangle

∴ AB = AC = BC

Now, AB = AC

On Squaring both sides, we get

(*x* + 4)^{2} + (*y* – 3)^{2} = (*x* – 4)^{2} + (*y* – 3)^{2}

(*x* + 4)^{2} = (*x* – 4)^{2}

or *x*^{2} + 16 + 8*x* = *x*^{2} + 16 – 8*x*

⇒ 16*x* = 0

*x* = 0 ....(1)

AC = BC implies that

On squaring both sides, we get

16 + *y*^{2} + 9 – 6*y* = 64

*y*^{2} – 6*y* – 39 = 0

, as origin lies in the interior of the triangle

Third vertex

**
**