In a message dated 9/5/2013 9:00:27 A.M. Eastern Daylight Time, AnlytcPhil@aol.com writes:
 (0,-3), (-1/2,7/2) and (-7/2,1/2)

Plot the points, and connect them:

 

These green lines are the mid-segments of the triangle we are trying
to determine the coordinates of.

We remember that a mid-segment of a triangle (which joins the 
midpoints of two sides of a triangle) is parallel to the third 
side of the triangle.  The mid-segment is also 1/2 of the third
side , but we do not need that fact.

Through each of those points we will find the equation of the line 
paralell to the mid-segment joining the other two points:

We find the slope of the mid-segment joining

(0,-3) and  (,)

m = 

where (x1,y1) = (0,-3)
and where (x2,y2) = (,)

m =  =  =  = ÷ = × = × = -13

Now we find the equation of the line through the third point (,):

Point-slope formula:

y - y1 = m(x - x1)

where (x1,y1) = the third point (,)

y -  = -13(x - ())

y -  = -13(x + )

y -  = -13x - )

    y = -13x - 

    y = -13x - 45  

That line is the red one below:



-------------------

We find the slope of the mid-segment joining

(0,-3) and (,)

m = 

where (x1,y1) = (0,-3)
and where (x2,y2) = (,)

m =  =  =  =  = ÷ = -1

Now we find the equation of the line through the third point (,):

Point-slope formula:

y - y1 = m(x - x1)

where (x1,y1) = the third point (,)

y -  = -1(x - ())

y -  = -1(x + )

y -  = -x - )

    y = -x + 

    y = -x + 3  

 

That line is the second red one below:



-------------------

We find the slope of the mid-segment joining

(,) and (,)

m = 

where (x1,y1) = (0,-3)
and where (x2,y2) = (,)

m =  =  =  =  = 1

Now we find the equation of the line through the third point  (0,-3), :

Point-slope formula:

y - y1 = m(x - x1)

where (x1,y1) = the third point (,)

y - (-3)} = 1(x - 0)

y + 3 = x 

    y = x - 3  

 

That line is the second red one below:



Now we find the three points of intersection of the three pairs of
the lines

y = -13x - 45,  y = -x + 3, y = x - 3

Solve these three systems:

y = -13x - 45      y = -13x - 45      y = -x + 3   
y = -x + 3         y = x - 3          y = x - 3

You can do that.  They are

(-4,7),  (-3,-6), and (3,0)

Edwin