point-line-segment-line-and-ray MCQs for UPSC Prelims

25 practice questions on point-line-segment-line-and-ray from the Lines and Angles section of the UPSC Prelims syllabus. 25 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.

10 Easy 11 Medium 4 Hard

Sample questions

Q1
medium

Is $\overrightarrow{PQ}$ the same as $\overrightarrow{QP}$?

  1. A No, they start at different endpoints and go in opposite directions
  2. B Yes, both name the same ray
  3. C No, because $\overrightarrow{QP}$ is not a ray
  4. D Yes, because both contain the points $P$ and $Q$
Show answer and explanation

Correct answer: A - No, they start at different endpoints and go in opposite directions

In naming a ray the first letter is the endpoint, so $\overrightarrow{PQ}$ starts at $P$ and $\overrightarrow{QP}$ starts at $Q$, giving two different rays pointing opposite ways. Containing the same two labelled points is not enough to make them equal, and $\overrightarrow{QP}$ is a perfectly valid ray.

Q2
medium

Three distinct points $A$, $B$ and $C$ lie on one straight line. How many different line segments do they determine?

  1. A $2$
  2. B $3$
  3. C $4$
  4. D $6$
Show answer and explanation

Correct answer: B - $3$

Each pair of points gives one segment, and three points form the pairs $AB$, $BC$ and $AC$, so $3$ segments. Answering $2$ forgets the segment joining the outer two points, and $6$ counts each segment twice by treating $\overline{AB}$ and $\overline{BA}$ as different.

Q3
medium

Two sharp pencils make dots of different thickness at the same position on a page. What can be said about the points they represent?

  1. A Neither dot can represent a point
  2. B The thicker dot represents a bigger point
  3. C They represent the same point, because a point has no thickness
  4. D They represent different points, because the dots differ in size
Show answer and explanation

Correct answer: C - They represent the same point, because a point has no thickness

A point has no size, so the thickness of the drawn dot is only a limitation of the pencil. Both dots mark the same position and therefore the same point. Points cannot be bigger or smaller than one another, and a drawn dot is a perfectly normal way to show a point.

Q4
easy

How is a point usually named in geometry?

  1. A By a number, such as $1$
  2. B By two capital letters, such as $PQ$
  3. C By a single capital letter, such as $P$
  4. D By a single small letter, such as $p$
Show answer and explanation

Correct answer: C - By a single capital letter, such as $P$

A point is named with one capital letter, for example the point $P$. Small letters are usually kept for lines, two capital letters name a segment or ray, and numbers are used for measures rather than for naming points.

Q5
easy

How many lines can be drawn through two given distinct points?

  1. A None
  2. B Exactly two
  3. C Infinitely many
  4. D Exactly one
Show answer and explanation

Correct answer: D - Exactly one

Through two distinct points exactly one straight line can be drawn. Infinitely many lines pass through a single point, but adding a second point fixes the direction completely, so two lines through the same pair is impossible and at least one always exists.

Q6
easy

Is $\overline{AB}$ the same as $\overline{BA}$?

  1. A No, they name different segments
  2. B Yes, both name the same segment
  3. C Yes, but only if $A$ is to the left of $B$
  4. D No, because the order of letters changes the length
Show answer and explanation

Correct answer: B - Yes, both name the same segment

A segment is fixed by its two endpoints, so naming them in either order gives the same segment: $\overline{AB} = \overline{BA}$. The position of the letters on the page is irrelevant, and reversing the order certainly cannot change the length.

Q7
medium

How many different lines can be drawn through $4$ points, no three of which lie on the same straight line?

  1. A $6$
  2. B $8$
  3. C $12$
  4. D $4$
Show answer and explanation

Correct answer: A - $6$

Each pair of points determines one line, and $4$ points give $6$ pairs, so $6$ lines. Answering $4$ counts the points rather than the pairs, $12$ counts each line twice by treating the two orders as different, and $8$ matches neither count.

Q8
medium

Assertion (A): The length of a ray cannot be measured. Reason (R): A ray has one endpoint and extends endlessly in the other direction.

  1. A Both A and R are true, and R is the correct explanation of A
  2. B Both A and R are true, but R is not the correct explanation of A
  3. C A is true, but R is false
  4. D A is false, but R is true
Show answer and explanation

Correct answer: A - Both A and R are true, and R is the correct explanation of A

Both statements are true, and R explains A exactly: because one end never stops, there is no far endpoint to measure to. Option (b) fails because the endlessness is precisely the reason, and (c) and (d) fail because neither statement is false.

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