[2 Mark Question Answer]

Question 12 Marks

The points B and C have the co-ordinates (3, 2) and (0, 3). Find B', the image of B under the reflection in the x-axis and C', the image of C under the reflection in the line BB'.

Answer

B = (3, 2), Therefore, reflection of B in the x-axis is B'= (3,-2)
C = (0, 3), Therefore, reflection of C in the line B is C' = (6, 3).

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Question 22 Marks

A point R $(3,-2)$ is reflected in the origin as R'. Point Q $(-7, 1)$ is reflected in the x-axis as Q'. Write down the co-ordinates of R' and Q'. Calculate the distance R' Q'.

Answer

$R=(3,-2)$. Therefore, reflection of $R$ in the origin is $R^{\prime}=(-3,2)$
$Q=(-7,1)$. Therefore, reflection of $Q$ in the $x$-axis is $Q^{\prime}=(-7,-1)$
Distance between R' $Q ^{\prime}=\sqrt{(-7-(-3))^2+(-1-2)^2}$
$=\sqrt{(-4)^2+(-3)^2}$
$=\sqrt{16+9}$
$ =\sqrt{25} $
$ =5 \text { units }$

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Question 32 Marks

A point P is reflected in the x-axis to P'. P' is then reflected in the origin to P". If the co-ordinates of P' are (-3, 4). Find the co-ordinates of P and P". Write the single transformation that map P onto P".

Answer

P' = (-3, 4).
Therefore, the co-ordinates of P under reflection in the x-axis = (-3,-4)
and the co-ordinates of P" under reflection in the origin = (3,-4).
The single transformation = reflection in the y-axis.

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Question 42 Marks

Perform the following operation and state the single transformation that take place :
$M_x. M_o$ on $P (-1,-3)$

Answer

$M_x. M_o$ on $P (-1,-3)$
$=M_x.M_o ( -1,-3)$
$= M_x (-1, 3)$
$= (-1,-3);$ reflection in the y-axis

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Question 52 Marks

Perform the following operation and state the single transformation that take place :
$M_o.M_y$ on $B (4, 6)$

Answer

$M_o.M_y$ on $B (4, 6)$
$= M_0 .M_y {4, 6)$
$= M_0 (-4, 6 )$
$= (4,-6)$; reflection in the x-axis

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Question 62 Marks

Perform the following operation and state the single transformation that take place
$M_y.M_o $ on $A (-7, 3)$

Answer

$M_y.M_o$ on $A (-7, 3)$
$=M_y.M_0 (-7, 3)$
$= M_y (7,-3)$
$= ( -7,-3)$ ; reflection in the x-axis

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Question 72 Marks

Perform the following operation and state the single transformation that take place :
$M_x .M_y$ on $P (2,-5)$

Answer

$M_x .M_y$ on $P (2,-5)$
$= M_x.M_y (2,-5)$
$= M_x (-2,-5)$
$= (-2, 5)$ ; reflection in the origin

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Question 82 Marks

A point P (-8, 1) is reflected in the x-axis to the point P'. The point P' is then reflected in the origin to point P". Write down the co-ordinates of P". State the single transformation that maps P into P".

Answer

P = (-8, 1), therefore co-ordinates of P' under reflection in the x-axis = (-8, -1).
Hence, the co-ordinates of P" under reflection in the origin = (8, 1).
The single transformation = reflection in the y-axis.

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Question 92 Marks

Write down the co-ordinates of the image of the point $(-2, 4)$ under reflection in the origin and under reflection in the y-axis. What is the distance between the points of reflection?

Answer

Let $P$ be the point $=(-2,4)$.
Image under reflection in the origin $P ^{\prime}=(2,-4)$
Image under reflection in the $y$-axis $p^{\prime \prime}=(2,4)$
Distance between points of reflection
$=\sqrt{(4-(-4))^2+(2-2)^2}$
$ =\sqrt{8^2} $
$ =\sqrt{64} $
$=8 \text { units }$

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Mathematics [2 Mark Question Answer]

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