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.

Question

Philoid · Accepted Answer

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 =

Hence, our point is (, 6)