Line/Point Reflections/Symmetry

In geometry, a transformation is the mapping of a figure, called the preimage, to a corresponding figure called its image. Both the preimage and image are congruent.

One type of transformation is called a line reflection. When you are only dealing with points, this is called point reflection.

Reflections across:

the x-axis (x, y) –> (x, -y)               the y-axis (x, y) –> (-x, y)

y = x (x, y) –> (y, x)                         origin (x, y) –> (-x, -y)

Note: the values of x or y don’t have to be positive. Do not get confused with the signs! For example, when you reflect (-4, -4) across the x-axis, you would get (-4, 4). Therefore, you are only changing the sign of the y-coordinate.

Notice how the coordinates of triangle A’B’C’ are the same coordinates as triangle ABC,BUT the signs have been changed. Triangle ABC has been reflected in the origin.

Line Symmetry – when a line of reflection creates two congruent parts