Divide the line segment in the given ratio
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 with AB.
(iii) Along AX, draw 5 (= 3 + 2) arcs intersecting the ray AX at and
such that
(iv) Join .
(v) Through draw a line
parallel to
making
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 with AB.
(iii) Draw a ray BY, on opposite side of AX with respect to AB,parallel to AX by making an angle equal to
(iv) Draw arcs intersecting the ray AX at and ray BY at
such that
(v) Join 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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