Divide the line segment in the given ratio


Parallel Lines III - Concepts
Class - 8th DAV Subjects
 
 
Concept Explanation
 

Divide the line segment in the given ratio

Divide the line segment in the given ratio:

In this concept, we will learn the method of dividing a line segment internally in a given ratio.

Example: Divide a line segment of length 12 cm internally in the ratio 3 : 2.

SOLUTION:

Steps of construction:

(i) Draw a line segment AB = 12 cm, by using ruler.

(ii) Draw a ray making a suitable acute angle large angle BAX with AB.

(iii) Along AX, draw 5 (= 3 + 2) arcs intersecting the ray AX at large A_{1},A_{2},A_{3},A_{4} and large A_{5} such that large AA_{1}=A_{1}A_{2}=A_{2}A_{3}=A_{3}A_{4}=A_{4}A_{5}

(iv) Join large BA_{5}.

(v) Through large A_{3} draw a line large A_{3}P parallel to large A_{5}B making large angle AA_{3}P=angle AA_{5}B, intersecting AB at point P.

The point P so obtained is the required point, which divides AB internally in the ratio 3 : 2.

Alternative method for division of a line segment internally in a given ratio:

Use the following steps to divide a given line segment AB internally in a given ratio m : n where  m and n are natural numbers.

Steps of Construction:

(i) Draw a line segment AB of given length.

(ii) Draw a ray AX making a suitable acute angle large angle BAX with AB.

(iii) Draw a ray BY, on opposite side of AX with respect to AB,parallel to AX by making an angle large angle ABY equal to large angle BAX.

(iv) Draw arcs intersecting the ray AX at large A_{1},A_{2},.......,A_{m}, and ray BY at large B_{1},B_{2},.......,B such that

large AA_{1}=A_{1}A_{2}=.......=A_{m-1}A_{m}=BB_{1}=B_{1}B_{2}=......=B_{n-1}B_{n}

(v) Join large A_{m}B_{n}. Suppose it intersects AB at P.

The point P is the required point dividing AB in the ratio m : n internally.

 
 
 
 


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