In what ratio is the line segment joining the points P(3, –6) and Q(5, 3) divided by x-axis ?

Given: Two points are P(3, –6) and Q(5, 3)

Let the line segment P(3, –6) and Q(5, 3) is divided at point A (x, 0) by x-axis in ratio m:n

Using Section Formula, we have

Here, (x, y) = (x, 0); (x₁, y₁) = (3, -6) and (x₂, y₂) = (5, 3)

Taking

So,

⇒ 0 = 3m – 6n

⇒ 3m = 6n

Hence, the ratio is 2:1 and the division is internal.