Find the ratio in which the point P (x, 2) divides the line segment joining the points A (12,5) and B (4, -3). Also, find the value of x.

Here, given points are A (12,5) and B (4, -3) and let the point dividing the line joining two points be P(x,2)

Let the ratio be m:n

By section formula,

x = , y =

For point P(x,2),

x = …(1)

And 2 = …(2)

Solving 2 for finding ratio between m and n,

2 =

2(m + n) = -3m +5n

2m + 2n = -3m +5n

∴ 5m = 3n

∴ =

∴ m : n = 3 : 5

Now solving for equation 1, where m = 3 and n =5

x =

∴ x =

∴ x = 9

Hence, our point is (9, 2)