NCERT Exemplar Solutions
Class 10 - Mathematics - CHAPTER 10: Construction - Exercise 10.1Question 3
Class 10 - Mathematics - CHAPTER 10: Construction - Exercise 10.1
Question. 3
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, A₃, ... and B₁, B₂, B₃, ... are located at equal distances on rays AX and BY, respectively. Then the points joined are
A5 and B6
A6 and B5
A4 and B5
A5 and B4
Detailed Answer with Explanation:
Step 1: We want to divide the line segment AB in the ratio 5:6. This means that if we cut AB at some point P, then AP : PB = 5 : 6.
Step 2: To do this, we draw a ray AX from point A making an acute angle with AB. On this ray, we mark equal distances and label them as A₁, A₂, A₃, …
Step 3: Similarly, we draw another ray BY from point B parallel to AX. On this ray also, we mark equal distances and label them as B₁, B₂, B₃, …
Step 4: Now, to divide in the ratio 5:6, we need to take the 5th point on AX (that is A₅) and the 6th point on BY (that is B₆).
Step 5: Join A₅ to B₆. The line A₅B₆ will intersect AB at a point P. This point P divides AB in the required ratio 5:6.
Final Answer: The correct points to join are A₅ and B₆.