Transformations in math occur when there is a change in position, shape, or size. When you are playing with a jigsaw puzzle, you could move a puzzle piece by sliding it, flipping it, or turning it. Each of these moves is a transformation of the puzzle piece.
In a transformation, the original figure is a preimage and the resulting figure is an image.
A transformation is an isometry if the preimage and the image are congruent.
Types of transformations in math
A translation or slide is an isometry in which all points of a figure move the same distance and in the same direction.
A reflection is an isometry in which the preimage and the image have opposite orientations. In other words, the image appears backward.
A rotation is an isometry in which a figure has been rotated or turned around a point called center of rotation.
A dilation is a transformation whose preimage and image are similar. In general, a dilation is not an isometry. A dilation could be an enlargement or a reduction.