Draw a line segment of length 6 cm. Using compasses and ruler, find a point P on it which divides it in the ratio 3:4.

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Solution

A point P can be marked on a line segment of length 6 cm which divides the line segment in the ratio of 3:4 as follows.
Steps of construction are as follows:

(1) Draw line segment AB of length 6 cm and draw a ray AX making an acute angle with line segment AB.

(2)Locate 7 (3+4 ) points, $A_{1}, A_{2}, A_{3}, A_{4} \dots \dots A_{7}$ , on AX such that $A A_{1} = A_{1} A_{2} = A_{2} A_{3} = A_{3} A_{4} = A_{4} A_{5} = A_{5} A_{6} = A_{6} A_{7}$ .
(3)Join $B A_{7}$ .
(4)Through the point A₃, draw a line parallel to $B A_{7}$ (by making an angle equal to $A A_{7} B$
intersecting AB at point P.

Hence, $P$ is the point that divides line segment AB of length 6 cm in the ratio of 3: 4.

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