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GATE 2019 ME (ME2) – Question 28

Engineering Mathematics · Linear Algebra: Matrix algebra, systems of linear equations, eigen values and eigen vectors · 1 mark · Multiple choice

Find the transformation matrix reflecting a point in the xy-plane about y = x.

  1. $\begin{bmatrix}1&0\\0&-1\end{bmatrix}$
  2. $\begin{bmatrix}-1&0\\0&1\end{bmatrix}$
  3. $\begin{bmatrix}0&1\\1&0\end{bmatrix}$
  4. $\begin{bmatrix}0&-1\\-1&0\end{bmatrix}$

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Correct answer: (C) $\begin{bmatrix}0&1\\1&0\end{bmatrix}$

Explanation

Reflection about y = x swaps coordinates: $(x,y)\mapsto(y,x)$. Thus the matrix is $$\begin{bmatrix}0&1\\1&0\end{bmatrix}.$$ **C**. Points on the mirror line remain fixed.