Find the ratio in which the point divides the line segment joining the points

Let P divide AB internally in the ratio m:n.

Using the section formula,

Internal section formula, the coordinates of point P divides the line segment joining the point (x₁, y₁), (x₂, y₂) in the ratio m₁:m₂ internally is

We get;

On equating,

We get;

And

3m + 3n = 8m – 2n

5n – 5m = 0

n = m

And, 5m + 5n = - 60 + 18n

65m – 13n = 0

13(5m – n) = 0

5m – n = 0

Since,

m = n does not satisfy.

5m - n = 0

5m = n

Hence, the required ratio is 1:5.