Find the ratio in which the point P(m, 6) divides the join of A(– 4, 3) and B(2, 8). Also, find the value of m.
6 = (m1y2 + m2y1)/ m1 + m2
6 = (m1 × 8 + m2 3)/ m1 + m2
6 = (8m1 + 3m2 ) / m1 + m2
8m1 + 8m2 = 6(m1 + m2)
2m1 – 3m2 = 0
m1:m2 = 3:2
Now,
m = (m1x2 + m2x1)/ m1 + m2
m = (m1 × 2 + m2 (– 4))/ m1 + m2
m = (2m1 – 4m2 ) / m1 + m2
2m1 – 4m2 = m(m1 + m2 )
Putting the values of m1 & m2
m = – 2/5
Hence, 3:2, m = – 2/5