+0 Let's try this out with a particular triangle. Consider the triangle ABC with A = (5, 4), B = (-9, 6), and C = (1, -4).
(a) Let D, E, F be the midpoints of \(\overline{AB}\) , \(\overline{AC}\), \(\overline{CB}\) respectively. Find the equations of medians \(\overline{AD}\), \(\overline{BE}\), and \(\overline{CF}\)
+129881 I'll do one.....the calculation of the other two is similar
(The median to BC is AF , not CF)
Mid point of BC = [ (-9 + 1) /2 , (6 + -4) /2) = (-4, 1) = F (5,4) (-4,1)
Slope of a line through AF = ( 1 - 4) / (-4 - 5) = -3/-9 = 1/3
Equation of line containing median AF using the slope and (5,4) =
y = (1/3) ( x - 5) + 4
y = (1/3)x - 5/3 + 4
y = (1/3) x + 7/3
