Translations
Practise Foundation GCSE translations by reading column vectors and moving shapes on coordinate grids. Describe the movement from one shape to another, place translated images and find the vector that reverses a translation. Jump to the questions
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Worksheet preview and key skills
Worksheet preview
Eight questions cover describing and carrying out translations on integer coordinate grids, including movements across the axes.
Enter column vectors in five questions. In three grid questions, select where a marked vertex lands to preview the entire translated shape.
What you’ll practise
- Counting horizontal and vertical movement between matching vertices.
- Applying positive and negative translation components without changing a shape’s orientation.
- Reversing a translation by changing both component signs.
Use the interactive worksheet below, or read the Topic guide for the method and worked example.
Translations
Enter each translation as a column vector. For grid questions, select where the marked vertex lands, then check your answer.
Topic guide
What is a translation?
A translation slides every point of a shape the same distance in the same direction. The image has the same size, shape and orientation as the original: it is not turned or flipped.
Reading a column vector
The top component gives the horizontal movement: positive means right and negative means left. The bottom component gives the vertical movement: positive means up and negative means down.
Describing a translation
Choose a vertex on the original shape and find the matching vertex on the image. Count the horizontal movement, then the vertical movement. Write these numbers in a column vector, horizontal above vertical. Check that another matching pair gives the same movement.
Worked example: translating a triangle
A triangle has vertices (−2, 1), (0, 1) and (−1, 3). Translate it by the column vector with top component 3 and bottom component −2.
Move each vertex 3 units right and 2 units down. Add 3 to each x-coordinate and subtract 2 from each y-coordinate. The image has vertices (1, −1), (3, −1) and (2, 1). Join them in the same order to complete the translated triangle.
On the interactive grid, select the destination of the marked vertex P. The worksheet moves the entire polygon by that displacement. Check that every vertex has moved by the given vector before checking your answer.
Reversing a translation
If C moves to D by 3 units right and 2 units down, D moves back to C by 3 units left and 2 units up. The inverse column vector has top component −3 and bottom component 2. Change the sign of both components.
Common mistakes
- Do not swap the components: horizontal comes first.
- Count grid intervals, not grid lines. Crossing an axis does not change the counting rule.
- Compare matching vertices, not whichever two corners are nearest.
- Move every vertex by the same vector. Keep the image’s orientation unchanged.
- For the reverse journey, change both signs, not just one.