Transformations
Slide it, flip it, turn it, resize it. Four moves cover every exam question — and each one has a short list of details you must give when you "describe fully".
National curriculum KS3: identify and construct congruent and similar shapes, including by translation, rotation, reflection and enlargement1 · One shape, four moves
A transformation moves a shape without changing what it is. The original is the object (teal); the moved copy is the image (purple). Try each move on the triangle.
2 · Describing a transformation
Exam questions say "describe fully". Each move has its own required details — miss one and the mark is gone.
| Move | You must give | Example answer |
|---|---|---|
| Translation | the vector | translation by (3 over −2) |
| Reflection | the mirror line | reflection in the line x = 1 |
| Rotation | angle, direction, centre | rotation 90° anticlockwise about (0, 0) |
| Enlargement | scale factor, centre | enlargement scale factor 2, centre (0, 0) |
Which moves keep the shape the same size? Translation, reflection and rotation — the image is congruent to the object. Enlargement changes the size but keeps the proportions — the image is similar.
Worked examples
Translate triangle A by the vector (4 over −3).
Reflect the point (3, 2) in the y-axis, then in the x-axis.
Enlarge a 3 cm × 2 cm rectangle, scale factor 2. What happens to the area?
Quick check
What you've learned
Translation slides by a vector. Reflection flips in a mirror line. Rotation turns by an angle and direction about a centre. Enlargement multiplies lengths by a scale factor from a centre. The first three keep the shape congruent; enlargement makes it similar. To describe fully: vector; mirror line; angle + direction + centre; scale factor + centre.