Geometry Transformations Review

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

The vector for a translation to the right is of the form , where a is a positive number.

The rule is (x, y) → (-y, x).

The reflection of a point (x, y) across the x-axis is (x, -y).

The reflection of a point (x, y) across the y-axis is (-x, y).

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

The effect is (x, y) → (y, -x).

To find the image of a segment under reflection, reflect each endpoint of the segment across the line of reflection.

The coordinate transformation is (x, y) → (y, -x).

The distance between two points (x1, y1) and (x2, y2) is given by $$d = \sqrt{(x2 - x1)^2 + (y2 - y1)^2}$$ .