Fundamental Geometrical Concepts — Multiple Choice Questions

A ray has

1. one end point

2. two end points

3. no end point

4. none of these

Answer

A ray has exactly one end point, called its initial point, and extends endlessly in one direction.

Hence, option 1 is the correct option.

A line segment has

1. one end point

2. two end points

3. no end point

4. none of these

Answer

A line segment is the straight path between two fixed points, so it has two end points.

Hence, option 2 is the correct option.

A line has

1. one end point

2. two end points

3. no end point

4. none of these

Answer

A line extends endlessly in both directions, so it has no end points.

Hence, option 3 is the correct option.

Which of the following has a definite length?

1. a ray

2. a line

3. a line segment

4. none of these

Answer

A ray and a line extend endlessly, so their lengths cannot be measured. A line segment has two fixed end points and therefore a definite, measurable length.

Hence, option 3 is the correct option.

Which of the following can be drawn on a piece of paper?

1. a ray

2. a line segment

3. a line

4. a plane

Answer

A ray and a line extend endlessly, and a plane extends indefinitely in all directions, so none of these can be drawn completely on paper. Only a line segment, having a definite length, can be drawn fully on a piece of paper.

Hence, option 2 is the correct option.

How many lines can be drawn to pass through a point?

1. one only

2. two only

3. four only

4. an infinite number

Answer

Through a single given point, lines can be drawn in every possible direction, so an infinite number of lines can pass through it.

Hence, option 4 is the correct option.

How many lines can be drawn to pass through two given points?

1. one only

2. two only

3. four only

4. unlimited

Answer

Two distinct points fix a unique direction, so exactly one line can be drawn passing through them.

Hence, option 1 is the correct option.

Two lines may intersect

1. at one point

2. at two points

3. at an infinite number of points

4. none of these

Answer

Two lines in a plane, if not parallel, cross each other at one common point.

Hence, option 1 is the correct option.

The minimum number of points of intersection of three lines in a plane is

1. 3

2. 2

3. 1

4. 0

Answer

The minimum number of points of intersection occurs when all three lines are parallel to one another. Parallel lines never meet, so there are 0 points of intersection.

Hence, option 4 is the correct option.

The maximum number of points of intersection of three lines is

1. 1

2. 2

3. 3

4. unlimited

Answer

The maximum number of points of intersection occurs when no two of the three lines are parallel and no three lines pass through the same point. In that case each pair of lines meets at a distinct point, giving 3 points of intersection.

Hence, option 3 is the correct option.

How many rays can be drawn with a given point as initial point?

1. one only

2. two only

3. infinitely many

4. none of these

Answer

From a given point, a ray can be drawn in every possible direction, so infinitely many rays can be drawn with that point as their initial point.

Hence, option 3 is the correct option.

Two points in a plane determine

1. exactly one line segment

2. exactly two line segments

3. an infinite number of line segments

4. none of these

Answer

Two distinct points are the two end points of the straight path joining them, so they determine exactly one line segment.

Hence, option 1 is the correct option.