NCERT Solutions for Class 6 Maths Chapter 4 (Ex 4.1)
Exercise 4.1
1. Use the figure to name:
a) Use the figure to name five points.
Ans: A point is a notion that shows exact location in space.
It is required to name five points using the given figure.
Thus, by seeing the given figure it can be concluded that points are $O$, $B$, $C$, $D$, $E$.
b) Use the figure to name a line.
Ans: A straight 1-D figure that has no thickness and can be extended at both the ends is called a line.
It is required to name a line using the given figure.
Thus, by seeing the given figure it can be concluded that lines are $\overline {DE} $, $\overline {DB} $, $\overline {OB} $, $\overline {OE} $, $\overline {OC} $.
c) Use the figure to name four rays.
Ans: A ray has one fixed end point and one point can be extended indefinitely only in one direction.
It is required to name four rays using the given figure.
Thus, by seeing the given figure it can be concluded that four rays are $\overrightarrow {OD} $, $\overrightarrow {OE} $, $\overrightarrow {OC} $,$\overrightarrow {OB} $.
d) Use the figure to name five line segments.
Ans: A line segment is a part of a line that has two fixed endpoints and cannot be extended.
It is required to name five line segments using the given figure.
Thus, by seeing the given figure it can be concluded that five line segments are $\overline {DE} $, $\overline {OD} $, $\overline {OB} $, $\overline {OE} $, $\overline {OC} $.
2. Name the line given all possible (twelve) ways, choosing only two letters at a time from the four given.
Ans: A straight 1-D figure that has no thickness and can be extended at both the ends is called a line.
It is required to name all the possible lines from the four given points in the figure.
Choose point $A$ and write the lines formed by $A$ and other three points.
Therefore from the given figure it can be concluded that lines formed by using two letters at a time are $\overline {AB} $, $\overline {AC} $, $\overline {AD} $.
Choose point $B$ and write the lines formed by $B$ and other three points.
Therefore from the given figure it can be concluded that lines formed by using two letters at a time are $\overline {BC} $, $\overline {BD} $, $\overline {BA} $.
Choose point $C$ and write the lines formed by $C$ and other three points.
Therefore from the given figure it can be concluded that lines formed by using two letters at a time are $\overline {CD} $, $\overline {CB} $, $\overline {CA} $.
Choose point $D$ and write the lines formed by $D$ and other three points.
Therefore from the given figure it can be concluded that lines formed by using two letters at a time are $\overline {DA} $, $\overline {DB} $, $\overline {DC} $.
Thus, all the possible ways of naming lines are $\overline {AB} $, $\overline {AC} $, $\overline {AD} $, $\overline {BC} $, $\overline {BD} $, $\overline {BA} $, $\overline {CD} $, $\overline {CB} $, $\overline {CA} $, $\overline {DA} $, $\overline {DB} $, $\overline {DC} $.
3. Use the figure to name:
a) Use the figure to name the line containing point $E$.
Ans. It is required to name a line containing point $E$.
A straight 1-D figure that has no thickness and can be extended at both the ends is called a line.
To name the lines containing point $E$ see the given figure. From the figure it is seen that the line $\overline {AE} $ and $\overline {FE} $ contains point $E$.
b) Use the figure to name line passing through point $A$.
Ans. It is required to name a line containing point $A$.
A straight 1-D figure that has no thickness and can be extended at both the ends is called a line.
To name the lines containing point $A$see the given figure. From the figure it is seen that the line $\overline {AE} $ and $\overline {DE} $ contains point $A$.
c) Use the figure to name the line on which $O$ lies.
Ans. It is required to name the line on which $O$lies.
A straight 1-D figure that has no thickness and can be extended at both the ends is called a line.
To name the lines on which $O$ see the given figure. From the figure it is seen that $O$lies on line $\overline {OB} $ and $\overline {OC} $.
d) Use the figure to name two pairs of intersecting lines.
Ans. It is required to name two pairs of intersecting lines.
When two or more lines cross each other in a plane then the lines are called intersecting lines.
To name two pairs of intersecting lines see the given figure. From the figure it is seen that lines $\overline {AD} $ and $\overline {OC} $ cross each other and thus they are intersecting lines.
Another pair of lines that crosses each other is $\overline {AE} $ and $\overline {EF} $.
Therefore two pairs of intersecting lines are $\overline {AD} $, $\overline {OC} $ and $\overline {AE} $, $\overline {EF} $.
4. How many lines can pass through:
a) How many lines can pass through one given point?
Ans: It is required to write the number of lines that can pass through one given point.
Draw a figure with one point and number of lines that can pass through it.
Thus, it can be said that an infinite number of lines can pass through one given point.
b) How many lines can pass through two given points?
Ans: It is required to write the number of lines that can pass through two given points.
Draw a figure with two points and number of lines that can pass through it.
Thus, it can be said that only one line can pass through two given point.
5. Draw a rough figure and label suitably in each of the following cases:
a) Point $P$ lies on $\overline {AB} $.
Ans: It is required to draw a line $\overline {AB} $ containing point $P$.
Draw a line $\overline {AB} $ and a point $P$ on that line.
b) $\overline {XY} $and$\overline {PQ} $ intersecting at $M$ .
Ans: It is required to draw lines $\overline {XY} $ and $\overline {PQ} $ that intersects at point $M$.
Draw two lines $\overline {XY} $ and $\overline {PQ} $ such that they cross each other and label their point of intersection as $M$.
c) Line $l$ contains $E$ and $F$but not$D$.
Ans: It is required to draw lines $l$ that contains points $E$ and $F$ but not $D$.
Draw a line $l$such that points $E$ and $F$ lie on the line and point $D$ lies away from the line.
d) $\overline {OP} $and$\overline {OQ} $ meet at $O$ .
Ans: It is required to draw lines $\overline {OP} $and$\overline {OQ} $that meet at point $O$.
Draw two lines $\overline {OP} $ and $\overline {OQ} $ such that they meet each other and label their point as $O$.
6. Consider the following line $\overline {MN} $. Say whether the following statements are true or false in context of the figure given.
a) $Q$, $M$, $O$, $N$, $P$ are points on line $\overline {MN} $.
Ans: It is required to state whether the given statement “$Q$, $M$, $O$, $N$, $P$ are points on line $\overline {MN} $” is true or false.
From the given figure it can be seen that all the points lie on the line. Thus, the statement is true.
b) $M$, $O$, $N$are points on the line segment $\overline {MN} $.
Ans: It is required to state whether the given statement “$M$, $O$, $N$are points on line segment $\overline {MN} $” is true or false.
From the given figure it can be seen that all the points lie on the line segment thus the statement is true.
c) $M$and$N$are end points of line segment $\overline {MN} $.
Ans: It is required to state whether the given statement “$M$ and $N$are end points of line segment $\overline {MN} $” is true or false.
From the given figure it can be seen that the line segment$\overline {MN} $ has $M$ and $N$ as the end points thus the statement is true.
d) $O$and$N$are end points of line segment $\overline {OP} $.
Ans: It is required to state whether the given statement “$O$ and $N$are end points of line segment $\overline {OP} $” is true or false.
From the given figure it can be seen that the line segment $\overline {OP} $ has $O$ and $P$ as the end points not $O$ and $P$ thus the statement is false.
e) $M$is one end point of line segment $\overline {QO} $.
Ans: It is required to state whether the given statement “$M$ is one end point of line segment $\overline {QO} $” is true or false.
From the given figure it can be seen that the line segment $\overline {QO} $ has $O$ and $Q$ as the end points not $M$ thus the statement is false.
f) $M$is one point on ray $OP$.
Ans: It is required to state whether the given statement “$M$ is one point on ray $OP$” is true or false.
From the given figure it can be seen that ray $OP$ passes through point $N$ not $M$ thus the statement is false.
g) Ray $OP$ is different from ray $QP$.
Ans: It is required to state whether the given statement “Ray $OP$ is different from ray $QP$” is true or false.
From the given figure it can be seen that ray $QP$ is the ray with $Q$ as its fixed point, but in $OP$ fixed point is $O$. So they are two different rays and hence the statement is correct.
h) Ray $OP$ is same as ray $OM$.
Ans: It is required to state whether the given statement “Ray $OP$ is same as ray $OM$” is true or false.
From the given figure it can be seen that ray $OP$ and ray $OM$are two different rays and are in different directions thus the statement is false.
i) Ray $OM$ is not opposite to ray $OP$.
Ans: It is required to state whether the given statement “Ray $OM$ is not opposite to ray $OP$” is true or false.
From the given figure it can be seen that ray $OM$ and $OP$ both extend in opposite directions and hence are opposite to each other thus the statement is false.
j) $O$is not the initial point of $\overline {NP} $ and $\overline {NM} $.
Ans: It is required to state whether the given statement “$O$ is not the initial point of $\overline {NP} $and $\overline {NM} $” is true or false.
From the given figure it can be seen that $\overline {NP} $ does not pass through point $O$ and $\overline {NM} $ passes through $O$ but is not the initial point thus the statement is true.
What Will You Learn In NCERT Solution For Class 6 Maths Exercise 4.1?
The Chapter builds your base for Geometry; it teaches you the basic concepts of geometry in an interesting way. The very first question of Exercise 4.1 Class 6 shows a diagram, and you have to answer four things based on the diagram. In question number 2, you are given a diagram of a line with four points on it, and you have to name the line in twelve ways by choosing two letters at a time.
Similarly, in the third question, there is a figure, and you have to answer four questions based on that figure. Question 4 comprises of two questions- how many lines can pass through one given point and how many lines can pass through two given points.
In question 5, you have to make a figure to answer subparts of question 5. Question 6 is a true or false type question; there are 10 subparts from “a to j “and you have to tell whether the statement is true or false.
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