Question

To divide a line segment AB in the ratio 5:7, first ray AX is drawn so that ∠BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is
(a) 8
(b) 10
(c) 11
(d) 12

Answer 1

We know that, in order to divide a line segment AB in the ratio m : n (m, n are positive integers), first draw a ray AX such that ∠BAX is an acute angle and then mark points on ray AX at equal distances such that the minimum number of these points is m + n.

Here, m = 5 and n = 7

∴ m + n = 5 + 7 = 12

Thus, to divide a line segment AB in the ratio 5 : 7, first ray AX is drawn so that ∠BAX is an acute angle and then at equal distances points are marked on the ray AX such that the minimum number of these points is 12.

Hence, the correct answer is option (d).