Translations, Reflections, & Rotations

Front

What is a translation in geometry?

Back

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

Front

What is the transformation rule for translating a point (x, y) by (a, b)?

Back

(x, y) -> (x + a, y + b)

Front

What does it mean to reflect a figure over a line?

Back

To reflect a figure over a line means to create a mirror image of the figure across that line.

Front

What is the transformation rule for reflecting a point (x, y) over the x-axis?

Back

(x, y) -> (x, -y)

Front

What is the transformation rule for reflecting a point (x, y) over the y-axis?

Back

(x, y) -> (-x, y)

Front

What is a rotation in geometry?

Back

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

Front

What is the transformation rule for rotating a point (x, y) 90 degrees counterclockwise around the origin?

Back

(x, y) -> (-y, x)

Front

What is the transformation rule for rotating a point (x, y) 180 degrees around the origin?

Back

(x, y) -> (-x, -y)

Front

What is the transformation rule for rotating a point (x, y) 270 degrees counterclockwise around the origin?

Back

(x, y) -> (y, -x)

Front

How do you determine the translation rule from one triangle to another?

Back

By finding the change in x and y coordinates from corresponding points of the triangles.