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InterviewSolution
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If (-4, 0) and (4,0) are two vertices of an equilateral triangle, find the coordinates of its third vertex. |
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Answer» 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) ` `=>(x+4)^2+y^2 = (x-4)^2+y^2 ` `=>(x+4)^2 = (x-4)^2` `=>x^2+16+8x = x^2+16-8x` `=>16x = 0` `=>x = 0` Now, `AB = BC` `:. sqrt((x+4)^2+y^2) = 8` `=> (x+4)^2+y^2 = 64` `=>(0+4)^2+y^2 = 64` `=>y^2 = 64-16` `=> y = sqrt48 = 4sqrt3` So, coordinates of third vertex will be `A(0,4sqrt3)`. |
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