Question

To divide a line segment AB in the ratio 4 : 7, a ray AX is drawn first such that ∠BAX is an acute angle and then points A₁, A₂, A₃, ... are located at equal distances on the ray AX and the point B is joined to
(a) A₁₂
(b) A₁₁
(c) A₁₀
(d) A₉

Answer 1

To divide a line segment AB in the ratio m : n (m, n are positive integers), firstly draw a ray AX such that ∠BAX is an acute angle. Now, along AX mark off m + n points at equal distances.
Suppose these m + n points marked on ray AX be A₁, A₂, A₃, ..., A_m, A_{m + 1}, ..., A_{m + n.} Then, join B to A_{m + n}.

Here, m = 4 and n = 7

∴ m + n = 4 + 7 = 11

So, B is joined to the point A₁₁.

Thus, in order to divide a line segment AB in the ratio 4 : 7, a ray AX is drawn first such that ∠BAX is an acute angle and then points A₁, A₂, A₃, ... are located at equal distances on the ray AX and the point B is joined to A₁₁.

Hence, the correct answer is option (b).