Find the ratio in which P(4, m) divides the line segment joining the points A(2, 3) and B(6, –3). Hence find m.

The required line is shown below:

Using the section formula,

Coordinates of P which divides AB having points A(x₁, y₁) and B(x₂, y₂) in, say k:1, are given by:

According to our question,

For A(2, 3) and B(6, –3), and let the ratio be k: 1,

We get:

Equating the coefficients we get,

6k + 2 = 4k + 4
2k = 2
k = 1
and also,

Putting the value of k, we get,

m = 0