Draw seg AB of length 7.5 cm and divide it internally in the ratio 3 : 2.

Answer: Point C on AB with AC = 4.5 cm and CB = 3 cm.

Steps of construction:

1. Draw seg AB = 7.5 cm.
2. Draw ray AX making an acute angle with AB.
3. With any convenient radius, mark 5 (= 3 + 2) equal parts on AX: \(A_1, A_2, A_3, A_4, A_5\).
4. Join \(A_5B\). Through \(A_3\) draw a line parallel to \(A_5B\) meeting AB at C.

By the basic proportionality theorem, \(\dfrac{AC}{CB} = \dfrac{AA_3}{A_3A_5} = \dfrac{3}{2}\). Check: AC = 4.5 cm, CB = 3 cm. This is the same idea used in constructing similar triangles.

[Figure: seg AB with ray AX below it; five equal marks on AX; \(A_5B\) joined and the parallel through \(A_3\) cutting AB at C.]