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If P'(x', y') is the reflection of the point P(x, y) on the x-axis, then the matrix which describe the reflection of point P(x, y), in the x-axis is :
Question

If P'(x', y') is the reflection of the point P(x, y) on the x-axis, then the matrix which describe the reflection of point P(x, y), in the x-axis is :

A.

[0110]\begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \\​​

B.

[0110]\begin{bmatrix} 0 & -1 \\ -1 & 0 \end{bmatrix} \\​​

C.

[1001]\begin{bmatrix} -1 & 0 \\ 0 & -1 \end{bmatrix} \\​​

D.

[1001]\begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}​​

Correct option is D

Given:
Reflection is in the x -axis
Concept used:
Reflection of  P(x, y) in the  x -axis gives P'(x, -y) 
This corresponds to the matrix transformation:
[1001][xy]=[xy]\begin{bmatrix}1 & 0 \\0 & -1\end{bmatrix}\begin{bmatrix}x \\y\end{bmatrix}=\begin{bmatrix}x \\-y\end{bmatrix}​​
Therefore, the required matrix is:
[1001] {\begin{bmatrix}1 & 0 \\0 & -1\end{bmatrix}}​​
Correct answer is (d)

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