Matrix Transformations Practice Questions

A reflection in the line $y = 0$.

A rotation of $180^\circ$ about the origin.

An enlargement, centre the origin, with scale factor $4$.

Circle the transformation matrix that represents a rotation of $90^\circ$ clockwise about the origin.

• $\begin{pmatrix} 0 & 1 \\ -1 & 0 \end{pmatrix}$
• $\begin{pmatrix} 0 & -1 \\ 1 & 0 \end{pmatrix}$
• $\begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}$
• $\begin{pmatrix} 0 & 1 \\ 1 & 0 \end{pmatrix}$

Describe geometrically the single transformation represented by $\begin{pmatrix} -1 & 0 \\ 0 & 1 \end{pmatrix}$

The transformation matrix $T = \begin{pmatrix} 3 & 0 \\ -1 & 2 \end{pmatrix}$

Work out the image of the point $(-2,\ 4)$ under the transformation represented by $T$.

Work out the coordinates of the images of $A$, $B$ and $C$.

Describe geometrically the single transformation represented by $M$.

Describe geometrically the single transformation represented by $M^3$.

Write down the matrix representing transformation $A$ and the matrix representing transformation $B$.

Work out the single matrix that represents transformation $A$ followed by transformation $B$.

Describe geometrically the single transformation represented by your matrix in part (b).

Work out the values of $a$ and $b$.

Hence work out the image of the point $(0,\ 5)$ under the transformation represented by $M$.

Write down the matrix $M$.

Write down the coordinates of $B'$, the image of $B$.

Work out the matrix that maps the square $OA'B'C'$ back onto the unit square $OABC$.

Write down the matrix representing $P$ and the matrix representing $Q$.

Work out the single matrix that represents $P$ followed by $Q$, and describe geometrically the single transformation it represents.

Show that $Q$ followed by $P$ represents a different single transformation, and describe it geometrically.