Question 1023758
<pre>
{{{drawing(400,1100/3,-6,6,-5,6,grid(1),

line(-4,-1,3,4), line(3,4,4,-3),line(4,-3,-4,-1),

green(line(0,-2,3,4)), locate(.2,-1.5,"M(0,-2)"),
locate(3.1,4.4,"A(3,4)"), locate(-6,-1.1,"C(-4,-1)"),
locate(4,-3,"B(4,-3)")  )}}}

The median (the green line) connects the vertex
A(3,4) to the midpoint of the opposite side CB. 

We find the midpoint of CB using the midpoint
formula:

Midpoint = {{{M(matrix(1,3,(x[1]+x[2])/2, ",",(y[1]+y[2])/2))}}}

Midpoint = {{{M(matrix(1,3,((-4)+(4))/2, ",",((-1)+(-3))/2))}}}

Midpoint = {{{M(matrix(1,3,0/2, ",",(-4)/2))}}}

Midpoint = <b>M(0,-2)</b>

We find the equation of median AM.

We use the slope formula:

m = {{{(y[2]-y[1])/(x[2]-x[1])}}}

where (x<sub>1</sub>,y<sub>1</sub>) = A(3,4)

and where (x<sub>2</sub>,y<sub>2</sub>) = M(0,-2)

m = {{{((-2)-(4))/((0)-(3))}}}

m = {{{(-6)/(-3)}}}

m = <b>2</b>

Point-slope formula:

y - y<sub>1</sub> = m(x - x<sub>1</sub>)

where m=2 and (x<sub>1</sub>,y<sub>1</sub>) = (3,4)

y - 4 = 2(x - 3)

y - 4 = 2x - 6

    y = 2x - 2

Edwin</pre>