Centroid of triangle with complex coordinates

Centroid G(z) of the triangle ABC is the point of concurrence of medians of triangle ABC and is given by 

    Z=\[\frac{z_1+z_2+z_3}{3}\]

where \[ z_1=a+ib\]

         \[ z_2=c+id\]

         \[ z_3=x+iy\]  are  complex coordinates of triangle ABC.

If \[ z_1=1+2i\] ,\[ z_2=2+5i\] and \[ z_3=3+5i\]

then centroid  of triangle ABC  is givebn by \[ \frac{1+2i+2+5i+3+5i}{3}\]=\[ \frac{6+12i}{3}=2+4i\]

Posted on by