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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