Question

Given ΔABC with A(–4, –2), B(4, 4), and C(18, –8), write the equation for the line containing median segment The term is line segment CP. in slope intercept form

Answer 1

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:

$\displaystyle{ P=( \frac{-4+4}{2} , \frac{-2+4}{2} )=(0, 1)$.


The slope m of the line through CP can be found by the slope formula using points C(18, -8) and P(0, 1):

$\displaystyle{ m= \frac{y_2-y_1}{x_2-x_1}= \frac{-8-1}{18-0}= \frac{-9}{18}= \frac{-1}{2}$.


Now, we can write the equation of the line with slope -1/2, passing through
P(0, 1):

$y-1= \frac{-1}{2}(x-0)\\\\y= -\frac{1}{2}x+1$.


Answer: $y=-\frac{1}{2}x+1$