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.
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.
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.
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: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.
- 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.
y = 1x + 2 ∴
y = x + 2