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.

It moves the shape 'a' units horizontally and 'b' units vertically.

To rotate a point (x, y) around the origin by an angle θ, use the formulas: (x', y') = (x*cos(θ) - y*sin(θ), x*sin(θ) + y*cos(θ)).

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

The line of reflection is the line over which a shape is reflected to create a mirror image.

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

The scale factor is the ratio of the size of the image to the size of the original shape.

Add 3 to the x-coordinate and 4 to the y-coordinate: (x + 3, y + 4).