Consider the triangle $\mathrm{\Delta}ABC$ , which D is the midpoint of segment BC, and let the point G be defined such that $(GD)=\frac{1}{3}(AD)$ . Assuming that ${z}_{A},{z}_{B},{z}_{C}$ are the complex numbers representing the points (A, B, C):

a. Find the complex number ${z}_{G}$ that represents the point G

b. Show that $(CG)=\frac{2}{3}(CF)$ and that F is the midpoint of the segment (AB)

a. Find the complex number ${z}_{G}$ that represents the point G

b. Show that $(CG)=\frac{2}{3}(CF)$ and that F is the midpoint of the segment (AB)