Find the equation of the median which starts from the vertex A, of the triangle ABC. A(5,2), B(-3,7), C(1,-5)

Definition of a median in a triangle: Join the vertex with
the middle of the opposite side to the vertex of the
triangle.

In our case, the opposite side of the A vertex is
the BC side.

Let's denote the middle of the side BC, as
being the point M.

To write the equation of the line (AM),
we have to know the coordinates of the points A and M.

For
the moment, we know, from the enunciation, just the coordinates o fthe A
point.

To find the coordinates of the middle point M, we'll
use the formula:

xM=
(xB+xC)/2

xM=(-3+1)/2=-2/2

xM=-1

yM=(yB+yC)/2

yM=(7-5)/2

yM=2/2

yM=1

So,
the coordinates for the point
M are: M(-1,1).

We can find now the equation
of the line which is passing through the points A and
M.

(xM-xA)/(x-xA)=(yM-yA)/(y-yA)

(-1-5)/(x-5)=(1-2)/(y-2)

-6/(x-5)=-1/(y-2)

6(y-2)=(x-5)

6y-12-x+5=0

6y-x-7=0

6y=x+7

y=x/6
+ 7/6

(AM):6y-x-7=0 or y=x/6 +
7/6