You are Here: Home >< Maths

# Proving that Central Median of Triangle is... watch

1. Well, here I had a little homework - to prove that the central median line MN=AB/2,

which I did using vectors:
MN=MC+CN
MN=MA+AB+BN
When I sum the equations:
2MN=MC+MA+CN+BN+AB
As MC & MA and CN & BN have contrary directions, their sum is 0 and therefore:
2MN=AB
MN=AB/2
As I have no place to check if I did this right, please reply whether you think it's right or wrong.
NOTE: All of the above is in vectors, consider there's an arrow above MN, MA etc. I'm not quite familiar with latex
2. That's fine, although your wording here:
As MC & MA and CN & BN have contrary directions, their sum i 0 and therefore ...
is a bit dodgy. I mean it's correct, but the point is that M and N are defined so that AM=MC and BN=NC; in particular, AM=-CM and BN=-CN, hence the result. The only reason I say this is because you haven't said that MC and MA have the same length (which is obvious, but still worth mentioning to justify cancelling them out).
3. (Original post by nuodai)
That's fine, although your wording here:

is a bit dodgy. I mean it's correct, but the point is that M and N are defined so that AM=MC and BN=NC; in particular, AM=-CM and BN=-CN, hence the result. The only reason I say this is because you haven't said that MC and MA have the same length (which is obvious, but still worth mentioning to justify cancelling them out).
Thanks, I forgot to mention that here Though I wrote it in my homework.

### Related university courses

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: April 6, 2011
The home of Results and Clearing

### 1,075

people online now

### 1,567,000

students helped last year
Today on TSR

### University open days

1. Keele University
Sun, 19 Aug '18
2. University of Melbourne
Sun, 19 Aug '18
3. Sheffield Hallam University
Tue, 21 Aug '18
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams