Find the equations of the medians of the triangle with vertices (4,5), (2,-1), and (0,7).

Answer 1

this is easy using vectors. If we let the points be A,B,C, then if you extend the median from A to Ma to point D such that AMa = MaD you have a parallelogram with diagonal AD. AD = AB + AC = (-2,-6)+(-4,2) = (-6,-4)
So, the median AMa = A + (-3,-2) = (1,3)
The slope from A to Ma is 2/3
So the line through A with slope 2/3 is y-5 = 2/3 (x-4)

Now do the other two medians to points Mb and Mc