The triangle $A B C$, where $A$ is $(2,6), B$ is $(-3,5)$ and $C$ is $(4,7)$, is reflected in the $y$-axis to triangle $A^{\prime} B^{\prime} C^{\prime}$. Triangle $A^{\prime} B^{\prime} C^{\prime}$ is then reflected in the origin to triangle $A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}$.
i. Write down the co-ordinates of $A ^{\prime \prime}, B ^{\prime \prime}$ and $C ^{\prime \prime}$.
ii. Write down a single transformation that maps triangle $A B C$ onto triangle $A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}$.
i. Write down the co-ordinates of $A ^{\prime \prime}, B ^{\prime \prime}$ and $C ^{\prime \prime}$.
ii. Write down a single transformation that maps triangle $A B C$ onto triangle $A^{\prime \prime} B^{\prime \prime} C^{\prime \prime}$.
Exercise 12 (B) | Q 14 | Page 171
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(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.
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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