1fully worked

Describe fully $\begin{pmatrix}1&0\\0&-1\end{pmatrix}$.

1$(1,0)\to(1,0)$Image of $(1,0)$ = first column

2$(0,1)\to(0,-1)$Image of $(0,1)$ = second column

3reflection in the $x$-axisName it fully (line / direction / centre)

Check - Why is this a reflection in the $x$-axis (not the $y$-axis)?

A points on the $x$-axis stay fixed and the $y$-coordinate changes signB both coordinates change signC the matrix is the identityD it doubles every point

2you finish it

Describe fully $\begin{pmatrix}0&1\\1&0\end{pmatrix}$.

1$(1,0)\to(0,1)$Image of $(1,0)$ = first column

2$(0,1)\to(1,0)$Image of $(0,1)$ = second column

3Name it fully (line / direction / centre)

Check - A student said this was a rotation. What tells you it is a reflection?

A the coordinates simply swap; points on $y=x$ are unchangedB the determinant is 2C the matrix is not squareD nothing, it is a rotation

3you finish it

Describe fully $\begin{pmatrix}0&-1\\1&0\end{pmatrix}$.

1$(1,0)\to(0,1)$Image of $(1,0)$ = first column

2Image of $(0,1)$ = second column

3Name it fully (line / direction / centre)

Check - How do you know the rotation is anticlockwise, not clockwise?

A $(1,0)$ turns to $(0,1)$, which is a quarter-turn anticlockwiseB the numbers are negativeC all rotations are anticlockwiseD because the centre is the origin

4you do it all

Describe fully $\begin{pmatrix}-1&0\\0&-1\end{pmatrix}$.

1Image of $(1,0)$ = first column

2Image of $(0,1)$ = second column

3Name it fully (line / direction / centre)

Check - Why can you also NOT call this an enlargement?

A a $180^{\circ}$ rotation keeps every length and area the same; an enlargement would change sizeB the matrix has negative entriesC enlargements are always positiveD it maps the origin to itself