Transformations of shapes

Geometry and measures

Questions marked Higher are aimed at the Higher tier.

These are original practice questions, not a past paper. This site is independent and not affiliated with AQA or Pearson.

Shape $A$ has vertices $(1, 1)$, $(3, 1)$ and $(1, 2)$. Translate $A$ by $\begin{pmatrix} 4 \\ 1 \end{pmatrix}$.

Shape A on a coordinate grid

2 marks
Reflect shape $A$ in the $y$-axis.

2 marks
Reflect shape $A$ in the $x$-axis.

3 marks
Rotate shape $A$ $90°$ clockwise about the origin.

3 marks
Rotate shape $A$ $180°$ about the origin.

4 marks
Enlarge shape $A$ by scale factor $2$, centre the origin.

4 marks
Describe the single transformation that maps $A$ to $(1, -1)$, $(3, -1)$, $(1, -2)$. Then describe the single transformation that maps $A$ to $(2, 2)$, $(6, 2)$, $(2, 4)$. Higher

5 marks
Translate $A$ by $\begin{pmatrix} -1 \\ 3 \end{pmatrix}$. Then enlarge $A$, not the translated image, by scale factor $3$ with centre $(1, 1)$. The area of $A$ is $1$. Find the area of this enlargement. Higher

6 marks

Mark scheme

Answer. $(5, 2)$, $(7, 2)$ and $(5, 3)$
- Add $4$ to each $x$-coordinate and $1$ to each $y$-coordinate.
- $(5, 2)$, $(7, 2)$, $(5, 3)$
Answer. $(-1, 1)$, $(-3, 1)$ and $(-1, 2)$
- The $y$-coordinates stay the same and the $x$-coordinates change sign.
- $(-1, 1)$, $(-3, 1)$, $(-1, 2)$
Answer. $(1, -1)$, $(3, -1)$ and $(1, -2)$
- The $x$-coordinates stay the same and the $y$-coordinates change sign.
- $(1, -1)$, $(3, -1)$, $(1, -2)$
Answer. $(1, -1)$, $(1, -3)$ and $(2, -1)$
- The rule $(x, y) \to (y, -x)$ gives a $90°$ clockwise rotation.
- $(1, -1)$, $(1, -3)$, $(2, -1)$
Answer. $(-1, -1)$, $(-3, -1)$ and $(-1, -2)$
- Both coordinates change sign.
- $(-1, -1)$, $(-3, -1)$, $(-1, -2)$
Answer. $(2, 2)$, $(6, 2)$ and $(2, 4)$
- Multiply both coordinates by $2$.
- $(2, 2)$, $(6, 2)$, $(2, 4)$
Answer. Reflection in the $x$-axis. Enlargement scale factor $2$, centre $(0, 0)$.
- The image is the same distance below the $x$-axis, so it is a reflection in the $x$-axis.
- Each coordinate has doubled, so the enlargement has scale factor $2$ and centre the origin.
Answer. Translation: $(0, 4)$, $(2, 4)$, $(0, 5)$. Enlargement: $(1, 1)$, $(7, 1)$, $(1, 4)$. Area $9$.
- The translation subtracts $1$ from $x$ and adds $3$ to $y$.
- From centre $(1, 1)$, the vectors to the other vertices are trebled.
- The enlargement has vertices $(1, 1)$, $(7, 1)$ and $(1, 4)$.
- Area scale factor $= 9$, so the area is $9$.