A(-1, 8), B(4, -2) and C(-5, -3) are the vertices of a triangle, find the equation of the median through (-1, 8).
21x + y + 13 = 0
Let's assume median which passes through A cuts the line BC at D.
Co-ordinates of D
D is the midpoint of line BC
D(x,y) = (4−52,−2−32)=(−12,−52)
Equation of the line passing through (-1,8) and (−12,−52)
y−y1=y2−y1x2−x1(x−x1)
y−8=−52−8−12+1(x+1)
y−8=−5−162−1+22(x+1)
y−8=−211(x+1)
y−8=−21x−21
21x+y+13=0
Equation of the line (median) that passes through (-1,8) is
21x+y+13=0