Question

Find equations of medians of $\Delta ABC$ where co-ordinates of vertices are $(0,0)$ , $(6,0)$ , $(3,8)$

Answer 1

$\begin{array}{c}AB=D\left(3,0\right)\\ BC=E\left(4.5,4\right)\\ AC=F\left(1.5,4\right)\\ e{q}^{n}CDis\\ y-0=\frac{8-0}{3-3}\left(x-3\right)\\ x=3\\ e{q}^{n}ofAEis\\ y-0=\frac{4-0}{4.5-0}\left(x-0\right)\\ =\frac{4}{4.5}x\\ =\frac{8}{9}x\\ e{q}^{n}ofBF\\ y-0=\frac{4-0}{1.5-6}\left(x-6\right)\\ =-\frac{4}{4.5}\left(x-6\right)\\ =\frac{4}{4.5}\left(6-x\right)\\ =\frac{8}{9}\left(6-x\right)\end{array}$