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Reflection - of a point
A transformation where a point appears an equal distance on the other
side of a given line - the line of reflection.
Try this Drag the point L to move the line of reflection, or drag the point P.

In this transformation, we are given a point (P) and a line of reflection (the vertical line in the figure above) which acts like a mirror. The given point P is "reflected" in the mirror and appears on the other side of the line an equal distance it. Drag the point P to see this. The reflection of the point P over the line is by convention named P' (pronounced "P prime") and is called the "image" of point P.

In the figure above, click 'show distances'. You can see that by definition, the point P', image of P, is the same distance from the line as P itself. Another way to say this is that the line of reflection is the perpendicular bisector of the line segment PP'. Drag the point P and move the line by dragging L to see that this is always true.

Constructing the reflection

You can construct the reflection of a point using compass and straightedge. First construct the perpendicular from P to the line of reflection ( see Constructing a perpendicular through an external point). Then with the compass, mark off an equal distance along the perpendicular on the other side of the line.

Things to try

In the diagram above - click 'reset'
  1. Move the point P and note the motion of its image P'.
  2. Move the line of reflection by dragging L. Repeat the above.
  3. Click on 'reset' and 'show distances'. As you drag P, note that the line of reflection is always the perpendicular bisector of PP'.
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Other transformation topics