GCSE · Transformations

Translations & enlargementsExam-style questions

Column vectors as translations, enlargement by a positive, fractional or negative scale factor from a centre, finding the centre and scale factor from a picture, and why lengths scale but angles don't.

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14 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAll Level 1 Level 3 Level 4

1
The diagram shows triangle $P$ and triangle $Q$ .Describe fully the single transformation that maps triangle $P$ onto triangle $Q$ .
Level 4 · 3 marksTry it
2
The diagram shows triangle $M$ and the point $C$ .(a) Enlarge triangle $M$ by scale factor $-2$ , centre $C$ .

(b) Write down the coordinates of the image of the vertex $(3, 2)$ .
Level 4 · 3 marksTry it
3
Rectangle $R$ has vertices $(2, 2)$ , $(5, 2)$ , $(5, 4)$ and $(2, 4)$ .

Rectangle $R$ is enlarged by scale factor $3$ , centre the origin, to give rectangle $R'$ .

(a) Work out the perimeter of rectangle $R'$ .

(b) Work out how many times bigger the area of $R'$ is than the area of $R$ .

(c) Rectangle $R'$ is then translated by the vector $\begin{pmatrix} -4 \\ 1 \end{pmatrix}$ . Write down the coordinates of the image of the vertex $(6, 6)$ of $R'$ .
Level 4 · 5 marksTry it
4
The diagram shows triangle $A$ and triangle $B$ on a coordinate grid.Describe fully the single transformation that maps triangle $A$ onto triangle $B$ .
Level 4 · 3 marksTry it
5
Triangle $T$ has vertices $(4, 2)$ , $(8, 2)$ and $(4, 6)$ .

Triangle $T$ is enlarged by scale factor $-\tfrac12$ , centre the origin, to give triangle $T'$ .

Write down the coordinates of the vertices of $T'$ .
Level 4 · 2 marksTry it

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