Question

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

Answer 1

(A) A₅ and B₆

According to the question,

A line segment AB in the ratio 5:7

So, A:B = 5:7

Steps of construction:

1. Draw a ray AX, an acute angle BAX.

2. Draw a ray BY ||AX, angle ABY = angle BAX.

3. Now, locate the points A₁,A₂,A₃,A₄ and A₅ on AX and B₁,B₂,B₃,B₄,B₅ and B₆

(Because A:B = 5:7)

4. Join A₅B₆.

A₅B₆ intersect AB at a point C.

AC:BC= 5:6