Question

if A(-1,3),B(1,-1) and C(5,1) are the vertices of the triangle ABC, what is the length of the median through vertex A

Answer 1

5 units
Firstly, calculate the coordinates of the mid point, let it D which lies b/w B and C by the formula [(x1+x2)/2, (y1+y2)/2]. Then find the length of AD by the distance formula: √(x2-x1)^2+(y2-y1)^2 . Finally you'll get your answer.

Answer 2

The length of median is 5 units.

Solution:

First, let we find the ‘co-ordinates’ value of D.

So that we can find the “length of median”, the co-ordinates values of D are

$\left(\frac{1-1}{2}, \frac{3+-1}{2}\right)=0,1$

Therefore, the ‘co-ordinates’ of the value of D is (0, 1) after simplification.  

Hence, to find the length we use CD $=\sqrt{\left(x_{2}-x_{1}\right)^{2}+\left(y_{2}-y_{1}\right)^{2}}.$

Hence, the value of CD$=\sqrt{(5-0)^{2}+(1-1)^{2}}=\sqrt{25}=5$  

Now that we have known that, the length of the median through vertex A is of length 5 units.