Question

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

(A) A₅ and B₆ 

(B) A₆ and B₅ 

(C) A₄ and B₅ 

(D) A₅ and B₄

Answer 1

(A) A₅ and A₆ 

Given a line segment AB and we have to divide it in the ratio 5 : 6.

Steps of construction:

1. Draw a ray AX making an acute ∠BAX.
2. Draw a ray BY parallel to AX by making ∠ABY equal to ∠BAX.
3. Now, locate the points A₁, A ₂, A₃, A ₄ and A₅ (m= 5) on AX and B₁, B₂, B₃, B₄, B₅ and B₆ (n = 6) such that all the points are at equal distance from each other.
4. Join B₆A₅. Let it intersect AB at a point C.
   Then, AC:BC = 5:6