A transformation is a movement of a figure in a plane from its original position to a new position.
The original figure is called the, while the figure resulting from the transformation is called the. A point in the image is usually named by adding a prime symbol ( ) to the name of the point in the preimage. preimage image
In a rigid transformation, or isometry, the image is congruent to the preimage.
We will consider three basic isometries: translations, reflections and rotations.
A reflection in a line m (or flip over line m) is a transformation that maps (or matches up) any point P to a point so that these two properties are true. 1. If P is not on m, then 2. If P is on m, then
A figure has a line of symmetry if the figure can be mapped onto itself by a reflection in a line.
The previous statement is the formal definition of a line of symmetry, but it is much easier to think of a line of symmetry as the line where the figure can be folded and have the two halves match exactly.