[3 marks sum]

Question 13 Marks

Each of the points A (3, 0), B (7, 0), C (- 8, 0), D (- 7, 0) and E (0, 0) is reflected in x-axis to points A’, B’, C’, D’ and E’ respectively. Write the co-ordinates of each of the image points A’, B’, C’, D’ and E’.

Answer

The points are given :
$
A(3,0), B(1,0), C(-8,0), D(-7,0) \text { and } E(0,0)
$

This images will be when reflected in $x$-axis. $A^{\prime}(3,0), B^{\prime}(7,0), C^{\prime}(-8$, $0) D^{\prime}(-7,0)$ and $E^{\prime}(0,0)$ as the given points lie on $x$-axis.

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Question 23 Marks

The point P (3, – 8) is reflected in origin to point Q. The Point Q is further reflected in the x-axis to point R. Find :
(i) the co-ordinates of Q
(ii) the co-ordinates of R
(iii) the image of P (3, – 8) in the y-axis.

Answer

(i) The image of the given point $P(3,-8)$ when reflected in origin is Q whose co-ordinates will be $(-3,8)$.

(ii) The image of $Q(-3,8)$ when reflected in $x$-axis is $R$ whose coordinates will be $(-3,-8)$
(iii) Tlie image of $P (3,8)$ in $y$-axis is $R$ whose co-ordinates are $(-3,-$ 8).

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Question 33 Marks

A point A (- 5, 4) is reflected in y-axis to point B. The point B is further reflected in origin to point C. find :
(i) the co-ordinates of B
(ii) the co-ordinates of C
(iii) the image of A (- 5, 4) in x-axis.

Answer

(i) Image of point $A(-5,4)$, when reflected in $y$-axis, is $B$ whose coordinates will be $(5,4)$
(ii) Image of $B(5,4)$, when reflected in origin, is $C$ whose coordinates will be $(-5,-4)$
(iii) Image of $A(-5,4)$ in $x$-axis is $C$ whose co-ordinates are $(-5,-4)$

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Question 43 Marks

A point P (7,3) is reflected in the x-axis to point P’. The point P’ is further reflected in v-axis to point P” Find :
(i) the coordinates of P’
(ii) the co-ordinates of P”
(iii) the image of P (7, 3) in origin.

Answer

(i) Image of point $P(7,3)$, when reflected in $x$-axis, is $P^{\prime}$ whose coordinates will be $(7,-3)$

(ii) Image of point $P ^{\prime}(7,-3)$ when reflected in $y$-axis, is $P ^{\prime \prime}$ whose coordinates will be $(-7,-3)$
(iii) The image of $P (7,3)$ in origin is $P ^{\prime \prime}$ whose coordinates are $(-7,-$ 3).

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Question 53 Marks

In the given figure, find the image of the line segment $A B$ in the line PQ:

Answer

Steps of Construction :
(i) From $A$ and $B$, draw perpendiculars on $P Q$ intersecting $P Q$ at $L$ and $M$.
(ii) Produce $A L$ to $A^{\prime}$ such that $A L=L A^{\prime}$ and produce $B M$ to $B^{\prime}$ such that $B M=M B^{\prime} A^{\prime} B^{\prime}$ is the image of the line segment $A B$ in $P Q$.

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Question 63 Marks

Mark points A (4, 5) and B (− 5, 4) on a graph paper. Find A’, the image of A in x-axis and B’, the image of B in x-axis.
Mark A’ and B’ also on the same graph paper. Join AB and A’ B’ and find if AB = A’ B’?

Answer

The given points:
$A(4,5)$ and $B(-5,4)$ have been marked on the graph.

The image of $A$ in $x$-axis $A(4,-5)$ and image of $B$ in $x$-axis is $B^{\prime}(-5$, - 4) which have been also plotted on the same graph.
$A B$ and $A^{\prime} B^{\prime}$ are joined. We see that $A B=A^{\prime} B^{\prime}$.

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Question 73 Marks

If possible, draw a rough sketch of a quadrilateral which has exactly two lines of symmetry.

Answer

Since the quadrilateral has exactly two lilies of symmetry
$\therefore$ It must be a rectangle or a rhombus

Rhombus

Rectangle

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Question 83 Marks

Write capital letters A to Z of English alphabet; and in each case, if possible, draw the largest number of lines of symmetry.

Answer

Line or lines of symmetry' is possible in the following alphabets. For other alphabets, it is not possible

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MATHS [3 marks sum]

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