Question 322502
<pre><b>
{{{drawing(400,2400/7,-7,7,-2,10,

triangle(-4,7,4,7,0,1), locate(-6,7,"S(-4,7)"), locate(4.1,7,"T(4,7)") locate(0,1,"R(0,1)"),
graph(400,2400/7,-7,7,-2,10) )}}}

A median is a line segment drawn from a vertex to the midpoint of
the opposite side. 

So first let's find the midpoint of the side RT, using the
midpoint formula:

{{{midpoint}}}{{{""=""}}}{{{"("}}}{{{(x[1]+x[2])/2}}}{{{","}}}{{{(y[1]+y[2])/2}}}{{{")"}}}{{{""=""}}}{{{"("}}}{{{(0+4)/2}}}{{{","}}}{{{(1+7)/2}}}{{{")"}}}{{{""=""}}}{{{"("}}}{{{4/2}}}{{{","}}}{{{8/2}}}{{{")"}}}{{{""=""}}}{{{"("}}}{{{2}}}{{{","}}}{{{4}}}{{{")"}}} 

Let's call that point M for "Midpoint". So we plot M(2,4):

{{{drawing(400,2400/7,-7,7,-2,10,
red(line(2+.1,4,2-.1,4), line(2,4+.1,2,4-.1), line(2+.1,4+.1,2-.1,4-.1), line(2+.1,4-.1,2-.1,4+.1), locate(2.4,4,"M(2,4)")),
triangle(-4,7,4,7,0,1), locate(-6,7,"S(-4,7)"), locate(4.1,7,"T(4,7)") locate(0,1,"R(0,1)"),
graph(400,2400/7,-7,7,-2,10) )}}} 

Now we draw the line segment SM, which is the median. I'll draw it
in red:

{{{drawing(400,2400/7,-7,7,-2,10,
red(line(2+.1,4,2-.1,4), line(2,4+.1,2,4-.1), line(2+.1,4+.1,2-.1,4-.1), line(2+.1,4-.1,2-.1,4+.1), locate(2.4,4,"M(2,4)"), line(2,4,-4,7)),
triangle(-4,7,4,7,0,1), locate(-6,7,"S(-4,7)"), locate(4.1,7,"T(4,7)") locate(0,1,"R(0,1)"),
graph(400,2400/7,-7,7,-2,10) )}}} 

and we want to find the equation of the line that contains that median.

That is, we want to find the equation of the line through the points 
S(-4,7) and M(2,4).  That's the red line:

{{{drawing(400,2400/7,-7,7,-2,10,
red(line(2+.1,4,2-.1,4), line(2,4+.1,2,4-.1), line(2+.1,4+.1,2-.1,4-.1), line(2+.1,4-.1,2-.1,4+.1), locate(2.4,4,"M(2,4)")),
triangle(-4,7,4,7,0,1), locate(-6,7,"S(-4,7)"), locate(4.1,7,"T(4,7)") locate(0,1,"R(0,1)"),
graph(400,2400/7,-7,7,-2,10,-x/2+5) )}}}



Use the slope formula: 

{{{m}}}{{{""=""}}}{{{(y[2]-y[1])/(x[2]-x[1])}}}{{{""=""}}}{{{((4)-(7))/((2)-(-4))}}}{{{""=""}}}{{{(-3)/(2+4)}}}{{{""=""}}}{{{(-3)/6}}}{{{""=""}}}{{{-1/2}}}

Use the point-slope formula:

{{{y-y[1]}}}{{{""=""}}}{{{m(x-x[1])}}}

{{{y-7}}}{{{""=""}}}{{{-1/2}}}{{{(x+4)}}}

{{{y-7}}}{{{""=""}}}{{{-1/2}}}{{{x}}}{{{""-""}}}{{{2)}}}

{{{y}}}{{{""=""}}}{{{-1/2}}}{{{x}}}{{{""+""}}}{{{5)}}}

Edwin</pre>