NCERT Solutions Ganita Prakash Chapter 2 Sections 2.2 & 2.3 Line Segment and Line — In-text Questions
Book page 14 & 15 Updated on2026-09-05
Q1.
Mark any two points A and B on a sheet of paper. Try to connect A to B by various routes (Fig. 2.1). What is the shortest route from A to B?
Answer
The straight path from A to B is the shortest route. All the curved and bent routes are longer.
This shortest path from point A to point B — including A and B — is called the line segment AB (or BA). The points A and B are its end points.
A point, a line segment PQ, a line CD (arrows show it never ends) and a ray OA.
Why it happens: every bend forces you to travel sideways before you can come back towards B, and that extra sideways travel adds length. Only a path with no bends at all wastes nothing. That is why a taut thread between two nails, or a stretched rubber band, always becomes straight.
Try This: Join two points with a thread along a curvy route, then straighten the thread out. Compare its length with the straight distance — the thread is always longer.
Q2.
Imagine that the line segment from A to B (i.e., AB) is extended beyond A in one direction and beyond B in the other direction without any end. This is a model for a line. Do you think you can draw a complete picture of a line? No. Why?
Answer
No — a complete picture of a line can never be drawn.
A line has no end points. It goes on endlessly in both directions, so however long a paper you take, the line would still have to continue beyond both edges.
What we do instead: we draw only a part of the line and put small arrowheads at the two ends. The arrowheads are a promise that the line keeps going. That is why a line through A and B is written as AB with arrows above it, while the segment AB is written without arrows.
Remember: two points are enough to fix a line completely — through any two points there passes exactly one line.