Translation and reflection - KS2 Maths - Year 6

Transformation

Translations and reflections are examples of transformations of shapes.

If a shape is transformed, its position and/or size is changed.

Translation is when a shape slides across, up, down or diagonally, without rotating or flipping over.

This shape has moved 4 squares across and 1 square down.

Grid showing an L shape that has moved 4 squares to the right and 1 square down from its original position.

Reflection  is when a shape is reflected in a mirror line. It looks like the shape is flipped over.

The reflection is the same distance from the mirror line as the original shape.

Grid showing an L shape reflected counterpart, with a dashed line indicating the mirror line between the two shapes.

Quiz: Translating and reflecting shapes

Why not see how much you know about this topic already? Then work through the page and see if you can beat your score.

Translation

When you translate a shape, every point on the shape moves the same distance and in the same direction.

Translating a shape will not change the size of the shape or rotate it.

This triangle has been translated 4 squares to the right and 3 squares down.

An 8x8 coordinate grid showing triangle A with vertices at (1,5), (2,8), and (4,5). Dotted arrows show a movement of 4 units across and 3 units down, with the numbers 4 and 3 labelled on the arrows. A translated triangle B, in a different colour, is positioned at the new coordinates (5,2), (8,2), and (6,5), showing the translation of the shape.

The coordinates of the vertices of each triangle are:

Triangle A	(1, 5) (2, 8) (4, 5)
Triangle B	(5, 2) (8, 2) (6, 5)

Now, let's look at another example of translation. Look at how this shape has moved.

It has been translated 2 squares to the left and 3 squares up.

An 8x8 coordinate grid with quadrilateral A drawn using vertices at (5,2), (7,1), (6,4), and (8,3). A translated quadrilateral B, with a different colour, is positioned at vertices (3,5), (5,4), (4,7), and (6,6), showing the translation of the shape.

Let's complete the table below and work out the coordinates of the vertices of the translated shape B.

Shape A	(5, 2) (7, 1) (6, 4) (8, 3)
Shape B

First, look at the bottom left vertex of shape B. Reading from the horizontal axis, you can see it's on number 3.
Then look at the number on the vertical axis, it's on 5.
Make a note of the numbers in brackets like this (3, 5).
Next, follow the same process for the other vertices of the quadrilateral.

Here is the complete table with all the coordinates.

Shape A	(5, 2) (7, 1) (6, 4) (8, 3)
Shape B	(3, 5) (5, 4) (4, 7) (6, 6)

Reflection

Reflection is a type of transformation. It's like using a mirror.

When a shape is reflected an image of that shape is created.

It is like ‘flipping’ the shape over the line of reflection or 'mirror line'.

Each point on the original shape is the same distance from the line of reflection as the corresponding point on the image.

Triangle B is a reflection of Triangle A.

Do you notice that the matching vertices of each triangle are the same distances away from the mirror line?

Triangle A reflected as Triangle B showing distance from the mirror line of each shape is equal

Transformations on a four quadrant grid

Coordinates are used to show an exact position of a point on a grid.

This is a four quadrant coordinates grid with negative numbers on the horizontal x-axis and vertical y-axis.

The point where the x-axis and the y-axis cross is called the origin. The coordinates of this point are (0,0).

The x-axis and y-axis divide the grid into four quadrants.

A four quadrant coordinates grid. The axis crosses in the middle to form 4 quarters. They are labelled first, second, third and fourth quadrants. There is an arrow pointing to where the axis cross and labelled 'origin'.

Look at these right-angled triangles.

An 8x8 coordinate grid divided into four quadrants, with both positive and negative numbers labelled from 1 to 6 along the axes. A triangle labelled ‘A’ is positioned in the top quadrants. A second triangle labelled ‘B’ is shown in the quadrants below. Triangle B has moved 3 units to the right and 6 units down shown by dotted arrows.

Triangle A is positioned in the first and second quadrants.

The coordinates of triangle A are:

Triangle A

(-4, 5) (-4, 2) (1, 2)

The triangle is translated 3 units to the right (parallel to the x-axis) and 6 units down (parallel to the y-axis).

Every point has moved the same distance and the same direction.

The coordinates of triangle B are:

Triangle B

(-1, -1) (-1, -4) (4, -4)

Now look at this grid.

Parallelogram A is positioned in the first and fourth quadrants.

The coordinates of parallelogram A are:

Parallelogram A

(2, 5) (5, 3) (5, -4) (2, -2)

An 8x8 coordinate grid divided into four quadrants, with a mirror line along the 𝑦-axis. Two parallelograms are shown on the grid: one on the left side of the 𝑦-axis labelled 'B' and one on the right labelled 'A', reflecting each other across the axis. The parallelograms are symmetrical and 2 units each apart from the mirror line..

Can you see how the shape has been reflected in the mirror line on the y-axis?

Each point on parallelogram A is the same distance from the mirror line as the corresponding point on parallelogram B.

The co-ordinates of parallelogram B are:

Parallelogram B

(-2, 5) (-5, 3) (-5, -4) (-2, -2)

Example 1

Shapes can be reflected more than once using different mirror lines.

A shape could be reflected in the x-axis or the y-axis.

Look at the shape on this coordinates grid.

a 4 quadrant coordinates grid with each axis from -5 to 5, an 'L' shape drawn with vertices at (4, 0), (4, 1), (1, 1), (1, 4), (0, 4).

What shape does it make if it is reflected in the y-axis?

Example 2