Geometry - Transformations

A transformation in geometry is an operation that moves or changes a shape in some way, including translations, rotations, reflections, and dilations.

A translation is a type of transformation that slides a shape from one position to another without turning it. It is defined by a vector that indicates the direction and distance of the slide.

(x, y) → (x - 2, y + 3)

When a point (x, y) is reflected over the y-axis, its coordinates change to (-x, y).

(5, 2)

The three main types of transformations are translations, reflections, and rotations.

(x, y) → (x + 4, y - 2)

Two shapes are congruent if they have the same size and shape, meaning one can be transformed into the other through translations, rotations, or reflections.

A rotation is a transformation that turns a shape around a fixed point, known as the center of rotation, by a certain angle.

(x, y) → (-y, x)