Question

The vertices of $∆ABC$are $A(2,2),B(-4,-4)$ and $C(5,-8)$. Find the length of a median of a triangle, which is passing through the point $C.$

• A. $\sqrt{65}$
• B. $\sqrt{117}$
• C. $\sqrt{85}$
• D. $\sqrt{116}$

Answer 1

The correct option is C

$\sqrt{85}$

Explanation for the correct option:

We know that the median passing through $C$ will absolutely pass through the midpoint of $A$ and $B.$

Then by using the midpoint of $AB=\left[\frac{2-4}{2},\frac{2-4}{2}\right]=\left(-1,-1\right)$

Therefore, the distance between the point $C(5,-8)$and $(-1,-1)$ is

$$\begin{gathered} =\sqrt{{\left(-1-5\right)}^2+{\left(-1+8\right)}^2} \\ =\sqrt{36+49} \\ =\sqrt{85} \end{gathered}$$

Hence the correct option is $\mathrm{Option}\left(\mathrm{C}\right)$