To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A₁ , A₂ , A₃ , ... and B₁ , B₂ , B₃ , ... are located at equal distances on ray AX and BY, respectively. Then the points joined are
a. A₅ and B₆
b. A₆ and B₅
c. A₄ and B₅
d. A₅ and B₄

Solution:

It is given that

Line segment AB is divided in the ratio 5: 6

A: B = 5: 6

Steps of Construction:

1. Construct a ray AX and an acute angle BAX.

2. Construct a ray BY || AX and ∠ABY = ∠BAX.

3. Let us locate the points A₁, A₂, A₃, A₄ and A₅ on AX and B₁, B₂, B₃, B₄, B₅ and B₆ as A: B = 5: 6

4. Now join A₅B₆.

5. Here A₅ B₆ intersects AB at the point C.

AC: BC = 5: 6

Therefore, the points joined are A₅ and B₆.

✦ Try This: To divide a line segment AB in the ratio 3: 2, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A₁, A₂, A₃, ... and B₁, B₂, B₃, ... are located at equal distances on ray AX and BY, respectively. Then the points joined are

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 11

NCERT Exemplar Class 10 Maths Exercise 10.1 Problem 3

To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A₁ , A₂ , A₃ , ... and B₁ , B₂ , B₃ , ... are located at equal distances on ray AX and BY, respectively. Then the points joined are a. A₅ and B₆, b. A₆ and B₅, c. A₄ and B₅, d. A₅ and B₄

Summary:

To divide a line segment AB in the ratio 5 : 6, draw a ray AX such that ∠BAX is an acute angle, then draw a ray BY parallel to AX and the points A₁ , A₂ , A₃ , ... and B₁ , B₂ , B₃ , ... are located at equal distances on ray AX and BY, respectively. Then the points joined are A₅ and B₆

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