Determine 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.
Here, given points are A (-4, 3) and B ( 2, 8) and let the point dividing the line joining two points be P(m,6).
Let the ratio be m:n
By section formula,
x = , y =
For point P(m,6),
m = …(1)
And 6 = …(2)
Solving 2 for finding ratio between m and n,
6 =
6(m + n) = 8m +3n
6m + 6n = 8m +3n
∴ 2m = 3n
∴ =
∴ m : n = 3 : 2
Now solving for equation 1, where m = 3 and n =2
m =
∴ m =
∴ m =
Hence, our point is (, 6)