Chapter 10.5, Problem 31MS

Cake trisection. Imagine a cake in the shape of a triangle that is placed on the xy-plane with corners at the points $\text{A-}\left(\text{0, 0}\right)\text{, B}\left(\text{3, 6}\right)\text{, and C-}\left(\text{6, 0}\right)\text{.}$

You plan to cut the cake into three equal pieces that meet at the central point of the cake $\text{D-}\left(\text{3, 3}\right)$. Find an equation for the cutting line from A to D, for the cutting line from B to D. and for the cutting line from C to D.