Doubt from complex number

  • sir my doubt is to get ans by geomatry i know algebric approch
    but how prove that minimum distance from 4th point of coordinate of traingle comes out when 4th point is centroid..
    @Hari_Shankar sir , @Jagdish_Singh sir , @Sourav_Dey sir , @Sharad
    please help me out in proving the concept...

\textbf{ignore the above written question language}

  • sir my doubt is to get ans by geomatry i know algebric approch
    but how prove that minimum value of above will only come when z will lie on \textbf{centriod} of traingle..
    @Hari_Shankar sir , @Jagdish_Singh sir , @Sourav_Dey sir , @Sharad
    please help me out in proving the concept...

This is because for any point in the plane of \triangle ABC we have

PA^{2}+PB^{2}+PC^{2}=\dfrac{1}{3}[AB^2+BC^2+CA^2]+3PG^2 (this is an exercise in R S Aggarwal in the Coord Geo chapter)

So LHS is minimized when PG= i.e. when P and G coincide.

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