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 ______.

Options

• A₅ and B₆

• A₆ and B₅

• A₄ and B₅

• A₅ and B₄

Answer 1

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 `underlinebb(A_5 and B_6)`.

Explanation:

To divide line segment AB 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 taking ∠ABY equal to ∠BAX.
3. Divide AX into five (m = 5) equal parts AA₁, A₁A₂, A₂A₃, A₃A₄ and A₄A₅
4. Divide BY into six (n = 6) equal parts and BB₁, B₁B₂, B₂B₃, B₃B₄, B₄B₅ and B₅B₆.
5. Join B₆ A₅. Let it intersect AB at a point C. Then, AC : BC = 5 : 6