Question

If A(−2, 4), B(0, 0) and C(4, 2) are the vertices of a ∆ABC, find the length of the median through A.

Answer 1

Let D be the midpoint of BC.
So, the coordinates of D are
$$\begin{gathered} D\left(\frac{0+4}{2},\frac{0+2}{2}\right)\left[B\left(0,0\right)\text{and}C\left(4,2\right)\mathrm{i}.\mathrm{e},\left(x_1=0,y_1=0\right)\text{and}\left(x_2=4,y_2=2\right)\right] \\ \mathrm{i}.\mathrm{e}.D\left(2,1\right) \end{gathered}$$
Length of the median:

$$\begin{gathered} AD=\sqrt{{\left(2+2\right)}^2+{\left(1-4\right)}^2} \\ =\sqrt{{\left(4\right)}^2+{\left(-3\right)}^2} \\ =\sqrt{16+9} \\ =\sqrt{25} \\ =5\text{units} \end{gathered}$$