Geometry - Transformations

A transformation is an operation that moves or changes a shape in some way to produce a new shape.

The four main types of transformations are translation, rotation, reflection, and dilation.

Translation is a transformation that moves every point of a shape the same distance in a given direction.

A rotation is a transformation that turns a shape around a fixed point, called the center of rotation.

A reflection is a transformation that flips a shape over a line, creating a mirror image.

Rotating a point 180° about the origin means to turn the point to the opposite side of the origin, resulting in the coordinates being negated.

To translate the point (x,y) 2 units left and 3 units up, you use the rule (x,y) → (x - 2, y + 3).

The result of reflecting the point (3,4) over the y-axis is (-3,4).

A dilation with a scale factor of 2 enlarges the shape, making it twice as large in every dimension.

A rotation turns a shape around a point, while a reflection flips a shape over a line.