To divide a line segment PQ in the ratio 4:5, first, a ray PX is drawn so that ∠QPX is an acute angle and then at equal distances points are marked on the ray PX such that the minimum number of these points is:

We know that to divide a line segment PQ in the ratio m:n, first draw a ray PX which makes an acute angle QPX, then we are required to mark m + n points at equal distances from each other.

Here, m = 4, n = 5

So, the minimum number of these points = m + n = 4 + 5 = 9