Find the lengths of medians of the triangle with vertices A= (0,0) B=(0,6) and C=(4,4)?

Question

I know that median is the segment from each vertex to the midpoint of the opp. side.

can someone explain the steps clearly to me, math is not my "forte".

Answer 1

First, let find these midpoints:

The midpoints of AB is ((0+0)/2,(0+6)/2), so it is (0,3) (mark it M)

The midpoint of AC is ((0+4)/2,(0+4)/2), i.e. (2,2) (N)

The midpoint of BC is ((0+4)/2,(6+4)/2), (2,5) - P

Now lets find lengts of AP; BN and CM

The length of the line between two points (x1,y1) and (x2, y2) is

sqrt[(x1-x2)^2+(y1-y2)^2]

So use it here, and we have:

AP=sqrt[(0-2)^2+(0-5)^2]=sqrt(4+25)=sq...

BN=sqrt[(0-2)^2+(6-2)^2]=sqrt(4+16)=sq...

CM=sqrt[(4-0)^2+(4-3)^2]=sqrt(16+1)=sq...

I hope you understand this and good luck!