Here we want to find the equation of the line containing the median CP.
P, being the midpoint of AB can be found using the midpoint formula as:
[tex]\displaystyle{ P=( \frac{-4+4}{2} , \frac{-2+4}{2} )=(0, 1)[/tex].
The slope m of the line through CP can be found by the slope formula using points C(18, -8) and P(0, 1):
[tex]\displaystyle{ m= \frac{y_2-y_1}{x_2-x_1}= \frac{-8-1}{18-0}= \frac{-9}{18}= \frac{-1}{2} [/tex].
Now, we can write the equation of the line with slope -1/2, passing through
P(0, 1):
[tex]y-1= \frac{-1}{2}(x-0)\\\\y= -\frac{1}{2}x+1 [/tex].
Answer: [tex]y=-\frac{1}{2}x+1[/tex]
