GCSE Maths revision · Geometry and measures

Transformations

Foundation and Higher

The idea

Each transformation needs its full description. Reflection: the mirror line. Rotation: the angle, the direction and the centre. Translation: a column vector. Enlargement: the scale factor and the centre.

Name the transformation.
Give every detail it needs.
Check with tracing paper or by moving one vertex at a time.

Watch out A rotation without its centre, or a translation without its vector, loses marks.

See it worked

Worked exampleNon-calculator3 marks

This question is about translations.

(a) The point $A(2, 5)$ is translated to the point $A'(6, 1)$ . Write down the column vector of the translation.

(b) The point $B(-3, 2)$ is translated by the vector $\begin{pmatrix} -2 \\ 5 \end{pmatrix}$ . Write down the coordinates of the image of $B$ .

(c) Write down the column vector that translates $A'$ back to $A$ .

(a) Across: $6 - 2 = 4$ . Up: $1 - 5 = -4$ (down 4).
(b) $(-3 + (-2),\ 2 + 5) = (-5, 7)$ .
(c) Going back reverses the movement, so both components change sign.

Answer (a) $\begin{pmatrix} 4 \\ -4 \end{pmatrix}$ ; (b) $(-5, 7)$ ; (c) $\begin{pmatrix} -4 \\ 4 \end{pmatrix}$

Your turn

Question 1Non-calculator3 marks

Point P has coordinates ( $-3$ , 5). It is translated by the column vector (7, $-9$ ), meaning 7 units right and 9 units down. Write the coordinates of its image.

Question 2Non-calculator4 marks

Point A is $(3,-2)$ . Rotate A 90 degrees anticlockwise about the origin.

(a) Find the image coordinates.

(b) Find the image after another 90 degree anticlockwise turn.

Question 3Non-calculator4 marks

Triangle T has vertices (1, 2), (4, 2) and (1, 4).

(a) T is reflected in the line y = x. Write down the image of the vertex (4, 2).

(b) T is rotated 180° about the origin. Write down the image of the vertex (1, 4).

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