Common Reflections
(KS3, Year 7)

The Lesson

A shape can be reflected in any line. The original shape is called the object, the reflected shape is called the image. The most common reflections are reflections in the x-axis (y = 0), the y-axis (x = 0), the line x = c, the line y = c, the line y = x and the line y = −x.

A Reflection in the X-Axis

The shape below has been reflected in the x-axis:

Each point on the image is the same perpendicular distance from the line of reflection as the object. Point A on the object is the same perpendicular distance from the line of reflection as the point A' on the image.

A Reflection in the Y-Axis

The shape below has been reflected in the y-axis:

Each point on the image is the same perpendicular distance from the line of reflection as the object. Point A on the object is the same perpendicular distance from the line of reflection as the point A' on the image.

A Reflection in the Line x = c

The shape below has been reflected in the line x = c:

Each point on the image is the same perpendicular distance from the line of reflection as the object. Point A on the object is the same perpendicular distance from the line of reflection as the point A' on the image.

A Reflection in the Line y = c

The shape below has been reflected in the line y = c:

Each point on the image is the same perpendicular distance from the line of reflection as the object. Point A on the object is the same perpendicular distance from the line of reflection as the point A' on the image.

A Reflection in the Line y = x

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

Each point on the image is the same perpendicular distance from the line of reflection as the object. Point A on the object is the same perpendicular distance from the line of reflection as the point A' on the image.

A Reflection in the Line y = −x

The shape below has been reflected in the line y = −x:

Each point on the image is the same perpendicular distance from the line of reflection as the object. Point A on the object is the same perpendicular distance from the line of reflection as the point A' on the image.

What Is a Reflection?

A reflection transforms a shape so that it becomes a mirror image of itself. By reflection, think of the reflection you would see in a mirror or in water. The orginal shape is called the object, the reflected shape is called the image:

It is as if the shape has been flipped. A reflection is a type of transformation.

Properties of Reflections

  • Each point in the image is the same perpendicular distance from the line of reflection as the corresponding point in the object.

    Point A' is the reflection of point A. They are both 3 squares away from the line of reflection. Point B' is the reflection of point B. They are both 1 square away from the line of reflection.
  • The image is the same size as the object.
  • If you were to fold the diagram along the line of reflection, the image would fit exactly over the object.
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See Also

What is geometry? What are transformations? What is the x-axis? What is the y-axis?