Invariant points and lines Quiz

1. Find the invariant points of $\begin{pmatrix}2&0\\0&1\end{pmatrix}$.

• A. Only the origin
• B. Every point on the $y$-axis
• C. Every point on the $x$-axis
• D. Every point

2. Which line is invariant under reflection in $y=x$?

• A. $y=2x$
• B. $y=-x$
• C. $y=x+1$
• D. $y=0$

3. Under $\begin{pmatrix}0&-1\\1&0\end{pmatrix}$ (rotation through $90^\circ$) how many invariant lines through the origin are there?

• A. None
• B. One
• C. Two
• D. Infinitely many

4. The matrix $\begin{pmatrix}1&0\\0&-1\end{pmatrix}$ has a line of invariant points. It is

• A. $y=x$
• B. $x=0$
• C. $y=-x$
• D. $y=0$

5. A point $P$ maps to $P'$ and the line $PP'$ has gradient $2$. If $PP'$ is an invariant line, its gradient is

• A. $2$
• B. $-2$
• C. $\frac12$
• D. unknown