Chapter 10: Constructions

(D) 12

According to the question,

A line segment AB in the ratio 5:7

So, A:B = 5:7

Now,

Draw a ray AX making an acute angle ∠BAX,

Mark A+B points at equal distance.

So, we have A=5 and B=7

Hence, minimum number of these points = A+B = 5+7 =12

(B) A₁₁

According to the question,

A line segment AB in the ratio 4:7

So, A:B = 4:7

Now,

Draw a ray AX making an acute angle BAX

Minimum number of points located at equal distances on the ray,

AX = A+B = 4+7= 11

A₁, A₂, A₃, ………. are located at equal distances on the ray AX.

Point B is joined to the last point is A₁₁.

(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