Invariant points and lines Quiz

1. Which point is invariant under $\begin{pmatrix}2&0\\0&1\end{pmatrix}$?

• A. $(1,0)$
• B. $(0,3)$
• C. $(2,1)$
• D. $(1,1)$

2. What is the line of invariant points of a reflection in the line $y=-x$?

• A. $y=x$
• B. The $x$-axis
• C. The $y$-axis
• D. $y=-x$

3. Which lines are invariant under an enlargement with centre the origin?

• A. Every line through the origin
• B. Only the axes
• C. Only $y=x$
• D. None

4. $\begin{pmatrix}1&3\\0&1\end{pmatrix}$ has the $x$-axis as a line of invariant points. Which line is invariant but not a line of invariant points?

• A. $y=x$
• B. $x=2$
• C. $y=2$
• D. $y=2x$

5. What are the gradients of the invariant lines through the origin of $\begin{pmatrix}3&1\\0&2\end{pmatrix}$?

• A. $0$ and $1$
• B. $0$ and $-1$
• C. $1$ and $2$
• D. $-1$ and $3$