Consider the triangle defined by A =(-2,0), B=( 6 , 0) and c =(4 ,6). Find an equation for the line that contains the median from the vertex B to AC.

Answer 1

A(-2,0) C(4,6)

AC has midpoint M(1,3) = averages of the x and y coordinates

from B(6,0) to (1,3) the line has slope = -3/5 = y/(x-6)

which is the equation of the median

y-0= (-3/5)(x-6) in point slope form

or

y-3 = (-3/5)(x-1) in point slope form using point M instead of point B

or

5y =-3x+18

or

3x+5y = 18 in standard form

or

3x+5y -18=0 in general form

or

y =-3x/5 +18/4 in slope intercept form

median length =

BM = .5sqr(2BA +2BC -AC)

=sqr34