To make a triangle with sides $\frac{8}{5}$of the corresponding sides of a given $∆\mathrm{ABC}$draw a ray $\mathrm{BX}$such that$\angle \mathrm{CBX}$is an acute angle and X is on the opposite side of A with respect to $BC.$The smallest number of points that must be located at equal distances along ray BX is

To divide a line segment in a predetermined ratio.

We want to divide a line segment AB in the ratio m: n, where m and n are both positive integers.

1) Draw a triangle $\mathrm{ABC}$.

2) Draw a line BX making an angle with $\mathrm{BC}$.

We will mark 8 points on the Ray BX and points are $B_1,B_2.B_3,B_4........B_8$