[2 Mark Question Answer]

Question 12 Marks

The point (-2, 0) on reflection in a line is mapped to (2, 0) and the point (5, -6) on reflection in the same line is mapped to (-5, -6).

(i) State the name of the mirror line and write its equation.

(ii) State the co-ordinates of the image of (-8, -5) in the mirror line.

Answer

(i) We know reflection of a point (x, y) in y-axis is (-x, y). Hence, the point (-2, 0) when reflected in y-axis is mapped to (2, 0). Thus, the mirror line is the y-axis and its equation is x = 0.

(ii) Co-ordinates of the image of (-8, -5) in the mirror line (i.e., y-axis) are (8, -5).

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Question 22 Marks

(i) Point $P(a, b)$ is reflected in the $x$-axis to $P^{\prime}(5,-2)$. Write down the values of $a$ and $b$.
(ii) $P ^{\prime \prime}$ is the image of P when reflected in the y -axis. Write down the co-ordinates of $P ^{\prime \prime}$.
(iii) Name a single transformation that maps $P ^{\prime}$ to $P ^{\prime \prime}$.

Answer

(i) We know $M _{ x }( x , y )=( x ,- y ) P ^{\prime}(5,-2)=$ reflection of $P ( a , b )$ in x -axis. Thus, the co-ordinates of P are $(5,2)$. Hence, $a =5$ and $b =2$.(ii) $P ^{\prime \prime}=$ image of $P (5,2)$ reflected in y -axis $=(-5,2)$
(iii) Single transformation that maps $P’$ to $P”$ is the reflection in origin.

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Question 32 Marks

State the co-ordinates of the following points under reflection in the line y = 0:

(i) (-3, 0)

(ii) (8, -5)

(iii) (-1, -3)

Answer

(i) (-3, 0)

The co-ordinate of the given point under reflection in the line y = 0 is (-3, 0).

(ii) (8, -5)

The co-ordinate of the given point under reflection in the line y = 0 is (8, 5).

(iii) (-1, -3)

The co-ordinate of the given point under reflection in the line y = 0 is (-1, 3).

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Question 42 Marks

State the co-ordinates of the following points under reflection in the line x = 0:

(i) (-6, 4)

(ii) (0, 5)

(iii) (3, -4)

Answer

(i) (-6, 4) The co-ordinate of the given point under reflection in the line x = 0 is (6, 4).

(ii) (0, 5) The co-ordinate of the given point under reflection in the line x = 0 is (0, 5).

(iii) (3, -4) The co-ordinate of the given point under reflection in the line x = 0 is (-3, -4).

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Question 52 Marks

State the co-ordinates of the following points under reflection in origin:

(i) (-2, -4)

(ii) (-2, 7)

(iii) (0, 0)

Answer

(i) (-2, -4) The co-ordinate of the given point under reflection in origin is (2, 4).

(ii) (-2, 7) The co-ordinate of the given point under reflection in origin is (2, -7).

(iii) (0, 0) The co-ordinate of the given point under reflection in origin is (0, 0).

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Question 62 Marks

State the co-ordinates of the following points under reflection in y-axis:

(i) (6, -3)

(ii) (-1, 0)

(iii) (-8, -2)

Answer

(i) (6, -3) The co-ordinate of the given point under reflection in the y-axis is (-6, -3).

(ii) (-1, 0) The co-ordinate of the given point under reflection in the y-axis is (1, 0).

(iii) (-8, -2) The co-ordinate of the given point under reflection in the y-axis is (8, -2).

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Question 72 Marks

Complete the following table.

Point	Transformation	Image
(5,-7)		(-5,7)
(4,2)	Reflection in x-axis
	Reflection in y-axis	(0,6)
(6,-6)		(-6,6)
(4,-8)		(-4,-8)

Answer

Point	Transformation	Image
(5,-7)	Reflection in origin	(-5,7)
(4,2)	Reflection in x-axis	(4,-2)
(0,6)	Reflection in y-axis	(0,6)
(6,-6)	Reflection in origin	(-6,6)
(4,-8)	Reflection in y-axis	(-4,-8)

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Question 82 Marks

The point $(-5, 0)$ on reflection in a line is mapped as $(5, 0)$ and the point $(-2, -6)$ on reflection in the same line is mapped as $(2, -6).(a)$ Name the line of reflection.
$(b)$ Write down the co-ordinates of the image of $(5, -8)$ in the line obtained in $(a).$

Answer

(a) We know that reflection in the line $x=0$ is the reflection in the $y$-axis.It is given that:
Point $(-5,0)$ on reflection in a line is mapped as $(5,0)$.
Point $(-2,-6)$ on reflection in the same line is mapped as $(2,-6)$.
Hence, the line of reflection is $x=0$.
(b) It is known that $M_y(x, y)=(-x, y)$ Co-ordinates of the image of $(5,-8)$ in the line $x=0$ are $(-5,-8)$.

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Question 92 Marks

Point $A(4,-1)$ is reflected as $A^{\prime}$ in the $y$-axis. Point $B$ on reflection in the $x$-axis is mapped as $B^{\prime}(-2,5)$. Write down the co-ordinates of $A^{\prime}$ and $B$.

Answer

Reflection in y -axis is given by $M _{ y }( x , y )=(- x , y ) A ^{\prime}=$ Reflection of $A (4,-1)$ in y -axis $=(-4,-1)$
Reflection in x -axis is given by $Mx ( x , y )=( x ,- y )$
$B^{\prime}=$ Reflection of $B$ in $x$-axis $=(-2,5)$
Thus, $B =(-2,-5)$

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Question 102 Marks

$P$ and $Q$ have co-ordinates $(-2,3)$ and $(5,4)$ respectively. Reflect $P$ in the $x$-axis to $P^{\prime}$ and $Q$ in the $y$-axis to $Q^{\prime}$. State the co-ordinates of $P ^{\prime}$ and $Q ^{\prime}$.

Answer

Reflection in x -axis is given by $M _{ x }( x , y )=( x ,- y ) P ^{\prime}=$ Reflection of $P (-2,3)$ in x -axis $=(-2,-3)$
Reflection in y -axis is given by $My ( x , y )=(- x , y )$
$Q^{\prime}=$ Reflection of $Q(5,4)$ in $y$-axis $=(-5,4)$
Thus, the co-ordinates of points $P ^{\prime}$ and $Q ^{\prime}$ are $(-2,-3)$ and $(-5,4)$ respectively.

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Question 112 Marks

The triangle $ABC$, where $A$ is $(2, 6), B is (-3, 5)$ and C is $(4, 7)$, is reflected in the y-axis to triangle$ A’B’C’.$ Triangle $A’B’C$’ is then reflected in the origin to triangle $A”B”C”.(i)$ Write down the co-ordinates of $A”, B”$ and $C”.$
(ii) Write down a single transformation that maps triangle ABC onto triangle $A”B”C”.$

Answer

(i) Reflection in $y$-axis is given by $M_y(x, y)=(-x, y) \therefore A^{\prime}=$ Reflection of $A(2,6)$ in $y$-axis $=(-2,6)$
Similarly, $B^{\prime}=(3,5)$ and $C^{\prime}=(-4,7)$
Reflection in origin is given by $M_O(x, y)=(-x,-y)$
$\therefore A ^{\prime \prime}=$ Reflection of $A ^{\prime}(-2,6)$ in origin $=(2,-6)$
Similarly, $B^{\prime \prime}=(-3,-5)$ and $C^{\prime \prime}=(4,-7)$
(ii) A single transformation which maps triangle $A B C$ to triangle $A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}$ is reflection in $x$-axis.

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Question 122 Marks

The point $A (4,6)$ is first reflected in the origin to point $A ^{\prime}$. Point $A ^{\prime}$ is then reflected in the y -axis to the point $A ^{\prime \prime}$.(i) Write down the co-ordinates of $A ^{\prime \prime}$.
(ii) Write down a single transformation that maps $A$ onto $A$ ".

Answer

(i) The reflection in origin is given by $M_O(x, y)=(-x,-y)$. $A^{\prime}=$ reflection of $A(4,6)$ in the origin $=(-4,-6)$ The reflection in $y$-axis is given by $M_y(x, y)=(-x, y) \cdot A^{\prime \prime}=$ reflection of $A^{\prime}(-4,-6)$ in the $y$-axis $=(4,-6)$ (ii) The reflection in $x$-axis is given by $M_x(x, y)=(x,-y)$. The reflection of $A(4,6)$ in $x$-axis is $(4,-6)$. Thus, the required single transformation is the reflection of $A$ in the $x$-axis to the point $A^{\prime \prime}$.

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Question 132 Marks

The point $A (-3, 2)$ is reflected in the x-axis to the point $A’$. Point A’ is then reflected in the origin to point $A”.(i)$ Write down the co-ordinates of $A”.$
$(ii)$ Write down a single transformation that maps A onto $A”.$

Answer

(i) The reflection in $x$-axis is given by $M_x(x, y)=(x,-y)$.
$A^{\prime}=$ reflection of $A(-3,2)$ in the $x$ - axis $=(-3,-2)$. The reflection in origin is given by $M_O(x, y)=(-x,-y) . A^{\prime \prime}=$ reflection of $A ^{\prime}(-3,-2)$ in the origin $=(3,2)$
(ii) The reflection in $y$-axis is given by $M_y(x, y)=(-x, y)$. The reflection of $A(-3,2)$ in $y$-axis is $(3,2)$. Thus, the required single transformation is the reflection of $A$ in the $y$-axis to the point $A^{\prime \prime}$.

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Question 142 Marks

The point $P(x, y)$ is first reflected in the $x$-axis and reflected in the origin to $P^{\prime}$. If $P^{\prime}$ has co-ordinates $(-8,5)$; evaluate $x$ and $y$.

Answer

$M_x (x, y) = (x, -y)M_O (x, -y) = (-x, y)$
Thus, we get the co-ordinates of the point $P’$ as $(-x, y)$. It is given that the co-ordinates of $P’$ are $(-8, 5).$
On comparing the two points, we get, $x = 8$ and $y = 5$

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Question 152 Marks

The point $(a, b)$ is first reflected in the origin and then reflected in the y-axis to $P’$. If $P’$ has co-ordinates $(4, 6)$; evaluate a and $b.$

Answer

$M_O (a, b) = (-a, -b)M_y (-a, -b) = (a, -b)$
Thus, we get the co-ordinates of the point $P^{\prime}$ as $(a, -b)$. It is given that the co-ordinates of $P^{\prime}$ are $(4,6)$. On comparing the two points, we get, $a=4$ and $b=-6$

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Mathematics [2 Mark Question Answer]

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