Math, asked by varshugowda985, 3 months ago

Division of a line segment in the given ratio. Draw a line segment
AB=10cm .Divide it in the ratio 3:4


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Answers

Answered by rutujapande09
0

Answer:

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Step-by-step explanation:

We follow the following step of construction.

Steps of construction

Step I

Drawn a line segment AB=10 cm by using a ruler.

Step II

Drawn any ray making an acute angle ∠BAX with AB.

Step III

Along AX, mark-off 5(=3+2) points A  

1

​  

,A  

2

​  

,A  

3

​  

,A  

4

​  

 and A  

5

​  

 such that

AA  

1

​  

=A  

1

​  

A  

2

​  

=A  

3

​  

A  

4

​  

=A  

4

​  

A  

5

​  

.

Step Iv

Join BA  

5

​  

 

Step v

Through A  

3

​  

 draw a line A  

3

​  

 P parallel to A  

5

​  

 B by making an angle equal to ∠AA  

5

​  

B at A  

3

​  

 intersecting AB at a point P.

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

ALTERNATIVE METHOD FOR DIVISION OF A LINE SEGMENT INTERNALLY IN A GIVEN RATIO

We may 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

Step I

Draw line segment AB of given length.

Step II

Draw any ray AX making an acute angle ∠BAX with AB.

Step III

Draw a ray BY, on opposite side of AX, parallel to AX by making an angle ∠BAY equal to ∠BAX.

Step IV

Mark off m points A  

1

​  

,A  

2

​  

,,A  

m

​  

, on AX and n points B  

1

​  

,B  

2

​  

,,B  

n

​  

 on BY such that

AA  

1

​  

=A  

1

​  

A  

2

​  

=.=A  

m−1

​  

A  

m

​  

 

=BB  

1

​  

=B  

1

​  

B  

2

​  

=.=Bn−1B  

n

​  

.

Step V

Join A  

m

​  

B  

n

​  

. Suppose it intersects AB at P.

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

In triangles AA  

m

​  

P and BB  

n

​  

P, we have  

∠A  

m

​  

 AP=∠PBB  

n

​  

  and, APA  

m

​  

=∠BPB  

n

​  

 

So, by AA similarly criterion, we have

△A A  

m

​  

P−△BB  

n

​  

P  

⇒  

BB  

n

​  

 

AA  

m

​  

 

​  

=  

BP

AP

​  

 

⇒  

BP

AP

​  

=  

n

m

​  

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