Find out the median of ABC triangle, which starts from vertex A, where A(1,2), B(2,3),C(2,-5).

Let's choose A1 as being the middle of the opposite side of A vertex, BC.

The coordinates of A1 are:

xA1=(xB+xC)/2=(2+2)/2=2

yA1= (yB+yC)/2=(3-5)/2=-1

In order to write the equation of the line AA1, we have to know also the slope mAA1=(yA1-yA)/(xA1-xA)

mAA1= (-1-2)/(2-1)=-3

The equation of the line which passes through the points AA1 and is the median of the side BC:

y-yA=mAA1*(x-xA)

Y-2=(-3)*(x-1)

y-2+3x-3=0

y+3x-5=0