A triangle has vertices at A(-3, 2), B(-5, -6), and C(5, 0). Determine the equation of the median from vertex A how do you find...

The  vertices of the triangle are A(-3, 2), B(-5, -6), and
C(5, 0).

To find the median from A, to the other side BC,
we have to find the mid point M of BC and then find the equation of the line through A
and M.

M(x , y) = ( (xB+xC)/2 ,
(yB+yC)/2)

xM = (-5+5)/2 =
0

xM = (-6 +0)/2 = -3.

M(x ,y)
=(0,-3)

Now we find the equation of the median AM, with
A(-3,2) and M(0,-3).

We know that the line joining the
points (x1 , y1) and (x2,y2) is:

y-y1 =
{(y2-y1(/(x2-x1)}(x-x1).

Therefore the equation of AM
is:-

y- -2) = {(-3-2)/(0 - 3)}(x-
-3)

y+2 =( 5/3 )(x+3)

3(y+2) =
5(x+2)

3y+6 =5x+10

5x-3y+10-6
=0

5x-3y+4 = 0

Therefore the
equation of the median is 5x-3y+4 = 0 is the equation of the median through the vertex A
of the triangle.