Question

The vertices of a triangle are A (-1,3) ,B (1,-1) and C (5,1). Find the length of the median through the vertex C

Answer 1

Coordinates of $A\equiv (-1,3)$

Coordinates of $B\equiv (1,-1)$

Coordinates of $C\equiv (5,1)$

The median through the vertex $C$ will meet at the mid point of $AB$.

Coordinate of mid-point on $AB=(\frac{(-1)+1}{2},\frac{3+(-1)}{2})=(0,1)$

Now,

Length of median through vertex $C=$ Distance between $(5,1)$ and $(0,1)$

Therefore,

Length of median $=\sqrt{{(0-5)}^2+{(1-1)}^2}$

$\Rightarrow$ Length of median $=\sqrt{{\left(5\right)}^2}=5\text{units}$

Hence the length of median through the vertx $C$ is $5$ units.