Geometry Transformations

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

To reflect a point (x, y) over the y-axis, change the sign of the x-coordinate: the image is (-x, y).

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

To translate the point (x, y) by (a, b), add a to the x-coordinate and b to the y-coordinate: the image is (x+a, y+b).

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

To rotate a point (x, y) 180° about the origin, change the signs of both coordinates: the image is (-x, -y).

The line of reflection y = x swaps the x and y coordinates of points: the image of (x, y) is (y, x).

To reflect a point (x, y) over the x-axis, change the sign of the y-coordinate: the image is (x, -y).

To reflect a point (x, y) over the y-axis, change the sign of the x-coordinate: the image is (-x, y).

The image of (3, 4) reflected over the line y = x is (4, 3).