Discussion
The transformation matrix \(\begin{bmatrix} 0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix}\) is used to obtain the reflection about the.......... .
Answer: C
The matrix gives the reflection about the diagonal line Y = -x.
Apply it to a point in homogeneous coordinates:
\[ \begin{bmatrix} 0 & -1 & 0 \\ -1 & 0 & 0 \\ 0 & 0 & 1 \end{bmatrix} \begin{bmatrix} x \\ y \\ 1 \end{bmatrix} = \begin{bmatrix} -y \\ -x \\ 1 \end{bmatrix} \]
The point (x, y) goes to (-y, -x), which is its mirror image in the line y = -x. For example (2, 0) goes to (0, -2).
Reflection about y = x swaps the coordinates without changing signs (the same matrix with +1s). Reflection about the y-axis has diagonal (-1, 1, 1), and about the line y = 0 (the x-axis) has diagonal (1, -1, 1).
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