Reflect a Point

A reflection is a kind of transformation. Conceptually, a reflection is basically a 'flip' of a shape over the line of reflection.

Reflections are opposite isometries, something we will look below.

Reflections are Isometries

Reflections are isometries . As you can see in diagram 1 below, $$ \triangle ABC $$ is reflected over the y-axis to its image $$ \triangle A'B'C' $$. And the distance between each of the points on the preimage is maintained in its image

The length of each segment of the preimage is equal to its corresponding side in the image .

$ m \overline = 3 \\ m \overline = 3 \\ \\ m \overline = 4 \\ m \overline = 4 \\ \\ m \overline = 5 \\ m \overline = 5 $

Though a reflection does preserve distance and therefore can be classified as an isometry, a reflection changes the orientation of the shape and is therefore classified as an opposite isometry.

You can see the change in orientation by the order of the letters on the image vs the preimage. In the orignal shape (preimage), the order of the letters is ABC , going clockwise.

On other hand, in the image, $$ \triangle A'B'C' $$, the letters ABC are arranged in counterclockwise order.