# To divide a line segment AB in the ratio p : q (p, q are positive integers), draw a ray AX so 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

a. greater of p and q

b. p + q

c. p + q - 1

d. pq

**Solution:**

Divide the line into n number of points which are equidistant

Here n = p + q

Now join the end of the __line segment__ at the nth point.

At the beginning A of line segment AB, construct a line parallel to that from N which cuts the original line segment AB

Here the minimum number of points required = p + q

Therefore, the minimum number of points is p + q.

**✦ Try This: **Draw the line segment AB = 10 cm in 3 equal parts.

**☛ Also Check:** NCERT Solutions for Class 10 Maths Chapter 11

**NCERT Exemplar Class 10 Maths Exercise 10.1 Sample Problem 1**

## To divide a line segment AB in the ratio p : q (p, q are positive integers), draw a ray AX so 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 a. greater of p and q, b. p + q, c. p + q - 1, d. pq

**Summary:**

To divide a line segment AB in the ratio p : q (p, q are positive integers), draw a ray AX so 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 p + q

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