Geometric Transformations

A geometric transformation is a function that moves or changes a shape in a specific way, such as translation, rotation, reflection, or dilation.

Translation is a transformation that moves every point of a figure the same distance in a specified direction.

Reflection is a transformation that flips a figure over a line, creating a mirror image.

Rotation is a transformation that turns a figure around a fixed point, called the center of rotation, by a certain angle.

Dilation is a transformation that changes the size of a figure but not its shape, by a scale factor.

To reflect a point (x, y) across the y-axis, the new coordinates become (-x, y).

To reflect a point (x, y) across the x-axis, the new coordinates become (x, -y).

The algebraic representation is (x, y) -> (-y, -x).

The new coordinates after a 90-degree clockwise rotation are (y, -x).

The new coordinates after a 90-degree counterclockwise rotation are (-y, x).