Common Reflections
(KS3, Year 7)

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:

reflect in 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:

reflect in 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:

reflect in 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:

reflect in 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:

reflect in 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:

reflect in 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:mirror_imageIt 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.properties_of_reflection_miniPoint 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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This page was written by Stephen Clarke.