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, .... and B₁, B₂,..... are located at equal distances on rays 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

To divide a line segment AB in the ratio m : n, draw a ray AX such that ∠BAX is an acute angle. Then draw a ray BY parallel to AX. The points A₁, A₂, ..., A_m and B₁, B₂, ..., B_n are located at equal distances on rays AX and BY respectively. Then the points A_m and B_n are joined to divide the line segment AB in the ratio m : n.



Here, m = 5 and n = 6

So, the points A₁, A₂, ..., A₅ and B₁, B₂, ..., B₆ are located at equal distances on rays AX and BY respectively. Then the points A₅ and B₆ are joined.

Thus, in order 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, ..., A₅ and B₁, B₂, ..., B₆ are located at equal distances on rays AX and BY respectively. Then the points joined are A₅ and B₆.

Hence, the correct answer is option (a).