Question

A segment with endpoints (-3, 9) and (2, -1) is reflected across the line y = x. Which matrix expression represents the transformation?
Answer choices:
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Answer 1

\(\begin{bmatrix} x_{1} &x_{2} \\ y_{1}&y_{2} \end{bmatrix}= \begin{bmatrix} 1 &-1 \\ 1 & 1 \end{bmatrix}\)

That's how you write the matrix and you multiply it with the following depending on the transformation you're doing:

If you're reflecting across the x-axis then you multiply it by
\(\begin{bmatrix} 1 & 0\\ 0 & -1 \end{bmatrix}\)

If you're reflecting across the y-axis then you multiply it by
\(\begin{bmatrix} -1 & 0\\ 0 & 1 \end{bmatrix}\)

If you're reflecting across the origin then you multiply it by
\(\begin{bmatrix} -1 & 0\\ 0 & -1 \end{bmatrix}\)

And finally, the one that's most pertinent to us:
If you're reflecting across the line y=x then you multiply it by
\(\begin{bmatrix} 0 & 1\\ 1 & 0 \end{bmatrix}\)