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If (-4, 0) and (4,0) are two vertices of...

If (-4, 0) and (4,0) are two vertices of an equilateral triangle, find the coordinates of its third vertex.

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Let `A(x,y)` is the coordinate of the third point.
We are given `B(-4,0)` and `C(4,0)`.
Here, `BC = sqrt(4-(-4)^2+(0-0)^2) = 8`
`AB = sqrt((x-(-4))^2+(y-0)^2) = sqrt((x+4)^2+y^2)`
`AB = sqrt((x-4))^2+(y-0)^2) = sqrt((x-4)^2+y^2)`
As given triangle is an equilateral triangle.
`:. AB = AC = BC`
` sqrt((x+4)^2+y^2) = sqrt((x-4)^2+y^2) `
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