The triangle $A (1, 2), B (4, 4)$ and $C (3, 7)$ is first reflected in the line $y = 0$ onto triangle $A^{'} B^{'} C^{'}$ and then triangle $A^{'} B^{'} C^{'}$ is reflected in the origin onto triangle $A^{''} B^{''} C^{''}$ . Write down the co-ordinates of :
(i) $A^{'}, B^{'}$ and $C^{'}$
(ii) $A^{''}, B^{''}$ and $C^{''}$ .
(2 Marks)

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Solution

Reflection in $y = 0$ means reflection in $x$ -axis.
(i) Since, reflection in the $x$ -axis is given by $M_{x} (x, y) = (x, - y)$
$∴ A^{'} =$ reflection of $A (1, 2)$ in the $x$ -axis $= (1, - 2)$
Similarly, $B^{'} = (4, - 4)$ and $C^{'} = (3, - 7)$
(1 Mark)

(ii) Since, reflection in the origin is given by $M_{o} (x, y) = (- x, - y)$
$∴ A^{''} =$ reflection of $A^{'} (1, - 2)$ in the origin $= (- 1, 2)$
Similarly, $B^{''} = (- 4, 4)$ and $C^{''} = (- 3, 7)$
(1 Mark)

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The triangle A(1,2),B(4,4) and C(3,7) is first reflected in the line y=0 onto triangle A′B′C′ and then triangle A′B′C′ is reflected in the origin onto triangle A′′B′′C′′. Write down the co-ordinates of : (i) A′,B′ and C′ (ii) A′′,B′′ and C′′. (2 Marks)