Problem $2($Three$-$Dimensional Extension$)$:

A stoplight is hung between three poles scattered around an intersection. The tops of the poles are located at the points $(1,1,9),(-1,1,8),$ and $(1,-1,10).$ The stoplight lies at the point $(x,y,6),$ lying within the triangle formed by the lines $x=1,y=1,$ and $y=-x.$ Assume the ropes are taught at any stoplight location $(x,y,6).$ At what coordinate $(x,y,6)$ will the tension magnitudes in each rope be equal $($up to a reasonably small error$)$ if the stoplight weighs $200$ N$?$