Question

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 exterior of the triangle.

Answer 1

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

Answer 2

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