Reflection - of a line segment

A transformation where every point on a line segment appears an equal distance on the other side of a given line - the line of reflection.
Try this drag the endpoints of AB, or drag the point L to move the line of reflection.

In this transformation, we are given a line segment AB and a line of reflection (the vertical line in the figure above) which acts like a mirror. Every point on the line segment AB is "reflected" in the mirror and appears on the other side of the line an equal distance from it. Drag either point A or B to see this.

The reflection of a point, say A, is usually named by adding a small dash and is written A'. This is pronounced "a prime". So the reflection of the line AB is named A'B'. The reflection is called the "image" of the line AB.

In the figure above, click 'show distances'. You can see that by definition, the point A' is the same distance from the line of reflection as A itself. The same is true for any other point of the line, such as B. Another way to say this is that the line of reflection is the perpendicular bisector of the a line linking two corresponding points.

Things to try

In the diagram above - click 'reset'
  1. Move the points A nad B, and note the motion of its image A'B'.
  2. Move the line of reflection by dragging L. Repeat the above.
  3. Click on 'reset' and 'show distances'. As you drag A or B, note that the line of reflection is always the perpendicular bisector of AA' and BB'.

Other transformation topics