# Division of a Line Segment

**To Divide a Line Segment in a Given Ratio**

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Divide a line segment of length 7 cm in the ratio 3:5 internally.

**Steps of Construction**

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1. Draw a line segment AB = 7 cm.

2. Draw a ray AX making an acute angleÂ âˆ BAXÂ with AB.

3. Along AX, mark off 8( = 3 + 5) pointsÂ A_{1}, A_{2}, A_{3}, A_{4}, A_{5}, A_{6}, A_{7}Â and A_{8}Â such that AA_{1Â Â }

=A_{1}A_{2}Â = A_{2}A_{3}Â = A_{3}A_{4}Â = A_{4}A_{5}Â = A_{5}A_{6}Â = A_{6}A_{7}Â = A_{7}A_{8}

4. Join A_{8}Â to B.

5. Through A_{3}, draw a line A_{3Â }PÂ ||A_{8Â }BÂ intersecting AB at P.

The point P is the desired point which dividesÂ AB internally in the ratio of 3 : 5.

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Divide a line segment of 5 cm length externally in the ratio of 2 : 3.

**Steps of Construction
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1. Draw the line segment AP = 5 cm.

2. Draw a ray AC making an acute angleÂ âˆ BACÂ with AB.

3. Along AC mark off 5 (equal to bigger numberÂ of ratio) points A_{1},A_{2},A_{3},A_{4}, and A_{5}Â such thatÂ AA_{1Â Â }=A_{1}A_{2}Â = A_{2}A_{3}Â = A_{3}A_{4}Â = A_{4}A_{5.}

4. Join A_{2}(= 5 - 3)th point to B.

5. Through A_{5}Â and parallel to A_{2}B draw a lineÂ A_{5}P intersecting the given line AB (produced)Â in P, P is the required point.