Geometry: Transformations
Transformations covers the four ways a shape can be moved or resized on a coordinate grid: translation (sliding using a vector), reflection (flipping in a mirror line), rotation (turning about a centre point) and enlargement (resizing using a scale factor and centre). Describing a transformation fully means stating its type plus all the details needed to reproduce it exactly, such as the vector, mirror line, angle and centre, or scale factor and centre.
Method
- Identify which of the four transformations has taken place by comparing the object and the image (same size and orientation but moved = translation; flipped = reflection; turned = rotation; different size = enlargement).
- For a translation, write the vector as (change in x, change in y), reading it from a chosen vertex to its image.
- For a reflection, identify the mirror line and check that each image point is the same perpendicular distance from the line as the object point.
- For a rotation, state the angle, the direction (clockwise or anticlockwise) and the centre of rotation.
- For an enlargement, find the scale factor by dividing a length on the image by the matching length on the object, and find the centre using ray lines through corresponding points.
- When describing a transformation fully, always give every required detail, not just the type.
Worked example
Triangle ABC has vertices A(2, 3), B(5, 3) and C(2, 6). Triangle ABC is enlarged by scale factor 2, centre (0, 0). Find the coordinates of A', B' and C'.
- For an enlargement centre the origin, multiply each coordinate of every vertex by the scale factor.
- A' = (2 x 2, 3 x 2) = (4, 6).
- B' = (5 x 2, 3 x 2) = (10, 6).
- C' = (2 x 2, 6 x 2) = (4, 12).
Practice questions
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Exam-style questions
Written in the style of a KS3 Maths exam paper, with a full mark scheme.
Point M has coordinates (6, -3). M is translated by the vector (-4, 2). Find the coordinates of the image.
Shape X has vertices (1, 1), (1, 3) and (3, 1). Shape Y has vertices (7, 1), (7, 3) and (5, 1). Describe fully the single transformation that maps shape X onto shape Y.
Triangle ABC has vertices A(1, 2), B(3, 2) and C(1, 5). Triangle ABC is enlarged by scale factor 3, centre (1, 2). Find the coordinates of A', B' and C'.
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