(22) geometry study guide given triangle abc with a(-4,-2) b (4,4) and c(18,-8) write the equation of the line containing the median that passes through point c in slope-intercept form.

y = (-1/2)x+1



Explanation:

D = Midpoint of A and B
D = (x,y)
x = [(xCoord of A)+(xCoord of B)]/2
x = [(-4)+(4)]/2
x = 0/2
x = 0
y = [(yCoord of A)+(yCoord of B)]/2
y = [(-2)+(4)]/2
y = 2/2
y = 1
So the midpoint of AB is D = (x,y) = (0,1)

The median for point C will go through the points D = (0,1) and C = (18,-8)

Let's find the slope of line DC
m = (y2-y1)/(x2-x1)
m = (-8-1)/(18-0)
m = -9/18
m = -1/2

Then use the slope m and one of the points D or C to find the y intercept b
I'm going to use the coordinates of point D
y = m*x+b
1 = (-1/2)*(0)+b
1 = 0+b
b = 1

So the equation of line DC is y = (-1/2)x+1, which contains the median that goes through point C