A translation moves every point by the same vector
This triangle is translated 2 right and 1 up, so each x-coordinate increases by 2 and each y-coordinate increases by 1.
OriginalImage
Translations do not turn or flip the shape. They just slide it.
Year 8
Translations, reflections and rotations
Describe and carry out translations, reflections and rotations by tracking what happens to every vertex on a coordinate grid.
Lesson overview
Geometry - transformations on a coordinate grid
A transformation changes the position of a shape but keeps its structure. A translation slides the shape. A reflection flips the shape in a mirror line. A rotation turns the shape around a centre. The key idea is that every vertex follows the same rule, so it helps to track the coordinates one point at a time.
A reflection swaps each point to the other side of the mirror line
This triangle is reflected in the y-axis, so the x-coordinates change sign but the y-coordinates stay the same.
OriginalReflected
Reflections keep the same distance from the mirror line on both sides.
A rotation turns the shape around the centre
A 90-degree clockwise rotation about the origin sends (x, y) to (y, -x).
OriginalRotated
The centre of rotation stays fixed. Every point turns through the same angle.
Worked example
Translate the square 2 right and 1 down.
OriginalImage
- Read the translation carefully: 2 right means add 2 to every x-coordinate.
- 1 down means subtract 1 from every y-coordinate.
- Move A(1,4) to A'(3,3), B(3,4) to B'(5,3), C(3,2) to C'(5,1), and D(1,2) to D'(3,1).
- Join the new points in the same order to make the translated image.
Try it
Think about what happens to the coordinates before choosing the answer. Track one point at a time if needed.
Question 1
Point A is at (2, 1). After a translation 3 right and 2 up, where is A'?
Question 2
What is the reflection of (4, -1) in the y-axis?
Question 3
What is the reflection of (-2, 3) in the x-axis?
Question 4
What is the image of (1, 2) after a 90-degree clockwise rotation about the origin?
Question 5
A shape is translated 4 right and 2 down. Which statement is correct?
Common mistakes
Watch for these when working through the lesson.
- Moving some vertices by a different amount from the others in a translation.
- Changing both coordinates in a reflection when only one should change sign.
- Rotating in the wrong direction or forgetting the centre of rotation.
Related topics
These ideas fit closely with this lesson.
- Plot and interpret linear graphs from y = mx + c.
- Angles in parallel lines.
- Volume of cuboids and prisms.