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To divide a line segment in a given ratio.

Given a line segment *AB*, we want to divide it in the ratio *m* : *n*, where both *m* and *n* are positive integers. To help you to understand it, we shall take *m* = 3 and *n* = 2.

**Steps of Construction:**

**Step I :** Draw any ray *AX*, making an acute angle with *AB*.

**Step II :**

Locate 5 (m+n) points A_{1},A_{2},A_{3},A_{4}, and A_{5}, on AX so that

AA_{1 }^{ }=^{ }A_{1}A_{2} =_{ }A_{2}A_{3 }=_{ }A_{3}A_{4 }= A_{4}A_{5 }

**Step III : Join B**A_{5. }

**Step IV :**

Through the point A_{3 }(m=3), draw a line parallel to A_{5}B(by

making an angle equal to ∠AA_{5)} intersecting AB at the point C (see fig.). Then ,AC : CB = 3 : 2.

Let us see how this method gives us the required division.

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