The Lesson

A shape can be reflected. Every point on the shape is reflected in a line of reflection. To describe a reflection, we need to say where the line of reflection is.

The Line of Reflection

The line of reflection is a mirror line. It is the line a shape is reflected in. The image below shows a shape reflected in a line of reflection.

How to Describe a Reflection

Describing a reflection is easy.

Question

Describe how the light blue shape below has been reflected to make the dark blue shape.

Step-by-Step:

1

Find a point on the shape and the corresponding point on its reflection.We will choose point A on the shape. Point A' is the corresponding point on the reflection.

2

Join the points with a line.

3

Mark the half way point of this line.

4

Find another point on the shape and the corresponding point on its reflection.We will choose point B on the shape. Point B' is the corresponding point on the reflection.

5

Join the points with a line.

6

Mark the half way point of this line.

7

Join the half way points with a line.
We have found the line of reflection. We can find the equation of the line.

8

Find the equation of the line. The equation of the line is y = x + 2.

Answer:

The shape has been reflected in the line y = x + 2:

Lesson Slides

The slider below shows another real example of how to describe a reflection.

What Is a Reflection?

A reflection flips a shape so that it becomes a mirror image of itself. A reflection is a type of transformation.

How to Find the Equation of a Line

It is useful to say what the equation of the line of reflection is. The equation of a line can be given in slope-intercept form:
y = mx + c
  • m is the slope (the steepness) of the line.
  • c is the y-intercept of the line: where the line crosses the y-axis.
Let us look at the example in this lesson.
  • The line goes up by 1 unit for every 1 unit it goes across. The line has a slope of 1.
  • The line crosses the y-axis at 2. It has a y-intercept of 2.
The equation of the line is:

y = 1x + 2 ∴

y = x + 2