NCERT Solutions Ganita Prakash Chapter 2 – 17Section 2.4 Ray — Figure it Out

Book page 15 Updated on2026-09-05

Q1.

Rihan marked a point on a piece of paper. How many lines can he draw that pass through the point? Sheetal marked two points on a piece of paper. How many different lines can she draw that pass through both of the points? Can you help Rihan and Sheetal find their answers?

Answer

Rihan can draw endlessly many lines (an uncountable number) through his single point.

Sheetal can draw only one line through her two points.

Why it happens: a single point does not fix a direction. Keep the pencil on that point and turn the ruler a little — you get a new line every time, and you can turn it by as small an amount as you like. But the moment a second point is fixed, the direction is decided as well, so the line has no freedom left.

Through 1 point → countless lines
Through 2 points → exactly 1 line

Check it yourself: put a ruler on two dots on your notebook. However you slide or turn it, you can draw only one straight line that touches both dots.

Q2.

Name the line segments in Fig. 2.4. Which of the five marked points are on exactly one of the line segments? Which are on two of the line segments?

Answer

Fig. 2.4 — the four line segments LM, MP, PQ and QR. L and R are free ends; M, P and Q are joints.

The four line segments are:

LM, MP, PQ and QR

Point	Segments it lies on	How many
L	LM	1
M	LM, MP	2
P	MP, PQ	2
Q	PQ, QR	2
R	QR	1

On exactly one segment: L and R. On two segments: M, P and Q.

Why: L and R are the two free ends of the zig-zag path, so only one segment reaches them. Every other point is a joint where two segments meet.

Q3.

Name the rays shown in Fig. 2.5. Is T the starting point of each of these rays?

Answer

Fig. 2.5 — the rays TA, TB and TN all start at T, but the ray NB starts at N.

The rays are TA, TB, TN and NB.

No, T is not the starting point of every ray.

T is the starting point of TA, TB and TN.
The starting point of NB is N, not T.

Why the order of letters matters: in the name of a ray the first letter is always the starting point and the second letter is any other point on it. So TB and NB run along the same straight path, but they are different rays because they start at different points.

Q4.

Draw a rough figure and write labels appropriately to illustrate each of the following: a. OP and OQ meet at O. b. XY and PQ intersect at point M. c. Line l contains points E and F but not point D. d. Point P lies on AB.

Answer

Rough figures for the four situations are shown below.

Rough figures for the four situations (a) to (d).

a. Two rays are drawn from the same starting point O — one through P, one through Q. Their common starting point O is where they meet.
b. Two lines XY and PQ are drawn crossing each other. The crossing point is labelled M.
c. A line is drawn and named l. Points E and F are marked on it, while D is marked away from it.
d. A line segment AB is drawn and P is marked as a point between A and B, on the segment itself.

Tip: a rough figure need not be neat or to scale — but the labels must be exactly where the question says. Put arrowheads on a line, dots at the ends of a segment, and one arrowhead on a ray.

Q5.

In Fig. 2.6, name: a. Five points b. A line c. Four rays d. Five line segments

Answer

Fig. 2.6 — D, E, O and B lie on one line; OC is a separate ray drawn from O.

In the figure, D, E, O and B lie on one straight line, and OC is a separate ray from O.

Part	Answer
a. Five points	D, E, O, B, C
b. A line	DB (it may also be named DE, DO, EO, EB or OB)
c. Four rays	OC, OB, OE, OD
d. Five line segments	DE, DO, DB, EO, EB (OB and OC are also correct)

Why so many names are possible: a line can be named using any two points on it, so the one straight line through D, E, O and B has several correct names. But a ray must always be named with its starting point first — every ray in this figure starts at O.

Q6.

Here is a ray OA (Fig. 2.7). It starts at O and passes through the point A. It also passes through the point B. a. Can you also name it as OB? Why? b. Can we write OA as AO? Why or why not?

Answer

Fig. 2.7 — the single ray that starts at O and passes through B and then A. It may be called OA or OB.

a. Yes, the same ray can be named OB.

A ray is named by its starting point followed by any other point lying on it. Here the starting point is O, and B lies on the ray just as A does. So OA and OB are two names for one and the same ray.

b. No, OA cannot be written as AO.

Ray OA — starts at O and goes past A, endlessly
Ray AO — starts at A and goes past O, in the opposite direction

Why it happens: unlike a line segment (where AB and BA mean the same thing), a ray has a definite starting point and a definite direction. Changing the order of the letters changes both. So OA ≠ AO.

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