In mathematics, a reflection is a mapping from a Euclidean space to itself that is an isometry with a hyperplane as a set of fixed points; this set is called the axis or plane of reflection. The image of a figure by a reflection is its mirror image in the axis or plane of reflection. Reflection is a change in the direction of a wavefront at an interface between two different media, so that wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves. We all have come across the word reflection in our daily lives. Reflection is nothing, but the mirror image of the object.
The law of reflection states that when a ray of light reflects off a surface, the angle of incidence is equal to the angle of reflection. In geometry, a reflection is a type of rigid transformation in which the pre-image is flipped across a line of reflection to create the image. Each point of the image is the same distance from the line as the pre-image is, just on the opposite side of the line.
A figure is said to be a reflection of the other figure, then every point in a figure is at equidistant from each corresponding point in another figure. The reflected image should have the same shape and size, but the image faces in the opposite direction. In reflection, translation may also take place because of its changes in the position. Here, the original image is called pre-image, and its reflection is called image. The representation of pre-image and image are ABC and A’B’C’ respectively. The reflection transformation may be about the coordinate system (X and Y-axis).
Reflection in a Point
A reflection point occurs when a figure is constructed around a single point known as the point of reflection or centre of the figure. For every point in the figure, another point is found directly opposite to it on the other side. Under the point of reflection, the figure does not change its size and shape.