A triangle $A B C$ where $A (- 2, 3), B (4, - 4) a n d C (6, - 7)$ is reflected in the x- axis onto $△ A^{'} B^{'} C^{'}$ and then is reflected in the origin onto $△ A " B " C "$ .Write down the co-ordinates of (i) $A^{'}, B^{'}, C^{'}$ and (ii) $A ", B ", C "$ .

$A ‘ (- 2, - 3), B ‘ (- 4, - 4), C ‘ (6, 7)$ ;
$A^{''} (2, 3), B^{''} (4, 4), C^{''} (6, 7)$

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$A ‘ (- 2, - 3), B ‘ (4, 4), C ‘ (6, 7)$ ;
$A^{''} (2, 3), B^{''} (- 4, - 4), C^{''} (- 6, - 7)$

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$A ‘ (- 2, - 3), B ‘ (4, 4), C ‘ (6, 7)$ ;
$A^{''} (- 2, - 3), B^{''} (- 4, 4), C^{''} (- 6, 7)$

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$A ‘ (2, 3), B ‘ (4, 4), C ‘ (6, 7)$ ;
$A^{''} (- 2, - 3), B^{''} (- 4, - 4), C^{''} (- 6, - 7)$

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Solution

The correct option is B
$A ‘ (- 2, - 3), B ‘ (4, 4), C ‘ (6, 7)$ ;
$A^{''} (2, 3), B^{''} (- 4, - 4), C^{''} (- 6, - 7)$

When a point is reflected in the x axis, the sign of its ordinate changes. Hence, the coordinates of $A^{'}, B^{'}, C^{'}$ are $A ‘ (- 2, - 3), B ‘ (4, 4), C ‘ (6, 7)$ respectively.
When a point is reflected in the origin, the sign of its ordinate and abscissa changes. Hence, the coordinates of $A ", B ", C "$ is the reflection of $A^{'}, B^{'}, C^{'}$ in origin.
Coordinates of $A ", B ", C "$ are $A^{''} (2, 3), B^{''} (- 4, - 4), C^{''} (- 6, - 7)$ respectively.

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