Median Formula/Examples/(1, -2), (-3,4), (2,2)

Example of Use of Length of Median of Triangle
Consider the triangle $\triangle ABC$ whose vertices are:
 * $A = \paren {1, -2}, B = \paren {-3, 4}, C = \paren {2, 2}$

The length of the median of $\triangle ABC$ which which bisects $AB$ is $\sqrt {10}$.

Proof
Let $\triangle ABC$ be embedded in a complex plane.

Let the position vectors of $A$, $B$ and $C$ be $z_1 = 1 - 2 i$, $z_2 = -3 + 4 i$, $z_3 = 2 + 2 i$ respectively.


 * Length-of-Triangle-Median-Complex-(1,-2),(-3,4),(2,2).png

Then:

Then:

Hence: