# Reflection

## Home learning focus

Learn about reflection of different shapes in geometry.

This lesson includes:

• a learning summary
• one activity sheet

# Learn

Students looking to achieve grade 4 in GCSE Maths must be able to draw an object reflected in a line of reflection.

Read page 1 of our 'Transformations' Bitesize revision guide to:

• understand what reflection is
• see some examples of reflections

## Reflection

If you look in a mirror, you see your own image. You (the object) and your image appear to be the same distance from the mirror.

A shape can be reflected across a line of reflection to create an image.

An object and its image are always the same perpendicular (meaning 'at right-angles to') distance from the line of reflection.

The line of reflection is also called the mirror line.

Reflection is an example of a transformation. A transformation is a way of changing the size or position of a shape.

In reflection, every point in the image is the same distance from the mirror line as the original shape. The size of the shape does not change.

Example

In this image the triangle PQR has been reflected in the mirror line to create the image P'Q'R'.

Note that each dotted line joining a point on the original shape to the same point on the image is perpendicular to the mirror line.

But mirror lines are not always horizontal. They can be vertical or on a diagonal, as in this example. Here you can see that line between R and R' in this image is perpendicular to the mirror line.

## The equation of the line of symmetry

To describe a reflection on a grid, the equation of the mirror line is needed.

Worked example

Reflect the shape in the line: x = -1.

The line x = -1 is a vertical line which passes through -1 on the x-axis.

Now you can reflect the shape across the line of reflection to create an image.

Remember: each point on an object and its corresponding points on its image are always the same perpendicular distance from the line of reflection. You can use this information to work out the reflection A'B'C' of the shape ABC.

# Practise

## Activity 1

Reflection

Complete the activity sheet from Beyond by Twinkl on reflection of shapes to test your knowledge. You can print it out or write your answers on a piece of paper.