iGCSE Mathematics (0580) - C7.1 Transformations- Exam Style Questions Paper 1- New Syllabus

Question

Shapes $A$ and $B$ are shown on the grid.

(a) Describe fully the single transformation that maps shape $A$ onto shape $B$.

(b) Draw the image of shape $A$ after a reflection in the line $y = -1$.

Most-appropriate topic codes (Cambridge IGCSE Mathematics 0580):

• TOPIC C7.1 Transformations: Recognise, describe and draw rotations (through multiples of $90°$) and reflections; questions will not involve combinations of transformations (Core)

▶️ Answer/Explanation

(a)
The transformation is a rotation.
The angle is $90°$ anticlockwise (equivalently, $270°$ clockwise).
The centre of rotation is $(0, 0)$.
✅ Answer: Rotation, $90°$ anticlockwise, centre $(0,\, 0)$.
Note: All three elements — type, angle/direction, and centre — must be stated for full marks.

(b)
To reflect in $y = -1$, each point $(x,\, y)$ maps to $(x,\,-2 – y)$.
$(1,\,1) \to (1,\,-3),\quad (3,\,1) \to (3,\,-3),\quad (3,\,2) \to (3,\,-4),\quad (1,\,2) \to (1,\,-4)$.
Draw the rectangle with vertices at $(1,-3)$, $(3,-3)$, $(3,-4)$, $(1,-4)$ on the grid.

✅ Answer: Rectangle with vertices at $(1,-3)$, $(3,-3)$, $(3,-4)$, $(1,-4)$.

Question

The grid shows two flags, $F$ and $A$.

(a) On the grid, draw the image of flag $F$ after a reflection in the line $x = -1$.

(b) On the grid, draw the image of flag $F$ after a rotation of $180°$ about $(0,\, 0)$.

(c) Describe fully the single transformation that maps flag $F$ onto flag $A$.

Most-appropriate topic codes (Cambridge IGCSE Mathematics 0580):

• TOPIC C7.1 Transformations: Recognise, describe and draw reflections, rotations and translations; describe a translation using a vector (Core)

▶️ Answer/Explanation

(a)
For a reflection in $x = -1$, each point $(x,\, y)$ maps to $((-2 – x),\, y)$. The image vertices are $(-4,\,5)$, $(-5,\,5)$, $(-4,\,4)$, $(-5,\,4)$, $(-4,\,2)$.
✅ Answer: Flag drawn with vertices at $(-4,5),\ (-5,5),\ (-4,4),\ (-5,4),\ (-4,2)$

(b)
For a rotation of $180°$ about the origin, each point $(x,\, y)$ maps to $(-x,\, -y)$. The image vertices are $(-2,\,-2)$, $(-2,\,-5)$, $(-3,\,-5)$, $(-3,\,-4)$, $(-2,\,-4)$.
✅ Answer: Flag drawn with vertices at $(-2,-2),\ (-2,-5),\ (-3,-5),\ (-3,-4),\ (-2,-4)$

(c)
Comparing flag $F$ at $(2,\,2)$ to the corresponding vertex of flag $A$ at $(4,\,-4)$, the shift is $+2$ in the $x$-direction and $-6$ in the $y$-direction — this is a translation.
✅ Answer: Translation by the vector $\dbinom{2}{-6}$

Question

(a) On the grid, draw the image of triangle $T$ after a rotation, $90^\circ$ clockwise, centre $(0, 0)$.

(b) Describe fully the single transformation that maps triangle $T$ onto triangle $A$.

(c) Describe fully the single transformation that maps triangle $T$ onto triangle $B$.

Most-appropriate topic codes (Cambridge IGCSE Mathematics 0580):

• C7.1 Transformations

▶️ Answer/Explanation

(a) Triangle $T$ has vertices at $(1,1)$, $(4,1)$, and $(1,3)$. Applying a $90^\circ$ clockwise rotation about origin rule $(x, y) \rightarrow (y, -x)$, the new coordinate points transform to $(1,-1)$, $(1,-4)$, and $(3,-1)$. Plot these points and connect them.

(b) Looking at triangle $T$ and $A$, they have identical orientation and size but have simply shifted positions. This is a translation. Let’s trace the movement from a corner of $T$ at $(1,1)$ to the corresponding corner of $A$ at $(-5,-3)$. It moves $6$ units left and $4$ units down, written as the column vector $\begin{pmatrix} -6 \\ -4 \end{pmatrix}$.
(c) Triangle $B$ is larger than $T$, meaning it’s an enlargement. Comparing side lengths, the bottom edge of $T$ is $3$ units while $B$ is $6$ units long, giving a scale factor of $2$. To find the centre of enlargement, draw straight lines through corresponding vertices until they intersect, which happens exactly at $(0,-2)$.
✅ Answer:
(a) Image drawn correctly with coordinates $(1,-1), (1,-4), (3,-1)$
(b) Translation by column vector $\begin{pmatrix} -6 \\ -4 \end{pmatrix}$
(c) Enlargement, scale factor $2$, centre $(0,-2)$

iGCSE Mathematics (0580) - C7.1 Transformations- Exam Style Questions Paper 1- New Syllabus

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