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 x2 + 16 + 8x = x2 + 16 – 8x

⇒ 16x = 0

x = 0  ....(1)

AC = BC implies that

On squaring both sides, we get

16 + y2 + 9 – 6y = 64

y2 – 6y – 39 = 0

, as origin lies in the interior of the triangle

Third vertex

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