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If $(-5,3)$ and $(5,3)$ are two vertices of an equilateral triangle, then find coordinates of the third vertex, given that origin lies inside the triangle. (Take $\sqrt{3}= 1.7$)
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Let the third vertex be $$\begin{aligned}& (x,y) \\ & A (-5,3) B(5,3) C(x,y) \\ & AB=10=AC \\ & AC^2=100 \\ & (-5-x)^2+(3-y)^2 = (5-x)^2+(3-y)^2 \\ & 20x =0 \\ & x=0 \\ & (3-y)^2=75 \\ & 3-y = \pm5\sqrt{3} \\ & y=3-5\sqrt{3} \\ & y= -5.5 \\ & \text{The coordinates of the third vertex are } (0,-5.5)\end{aligned}$$