SOLUTION: Given triangle ABC with coordinates A(3, 4), B(4, -3), and C(-4, -1) determine the equation of the line of the median from vertex A.

Algebra ->  Triangles -> SOLUTION: Given triangle ABC with coordinates A(3, 4), B(4, -3), and C(-4, -1) determine the equation of the line of the median from vertex A.      Log On


   

Question 1023758: Given triangle ABC with coordinates A(3, 4), B(4, -3), and C(-4, -1) determine the equation of the line of the median from vertex A.
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!


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 = 

Midpoint = 

Midpoint = M%28matrix%281%2C3%2C0%2F2%2C+%22%2C%22%2C%28-4%29%2F2%29%29

Midpoint = M(0,-2)

We find the equation of median AM.

We use the slope formula:

m = %28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29

where (x1,y1) = A(3,4)

and where (x2,y2) = M(0,-2)

m = %28%28-2%29-%284%29%29%2F%28%280%29-%283%29%29

m = %28-6%29%2F%28-3%29

m = 2

Point-slope formula:

y - y1 = m(x - x1)

where m=2 and (x1,y1) = (3,4)

y - 4 = 2(x - 3)

y - 4 = 2x - 6

    y = 2x - 2

Edwin