Rotations, Reflections, Translations

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, by a specified angle in a specified direction.

Front

How do you rotate a point 90º counterclockwise about the origin?

Back

To rotate a point (x, y) 90º counterclockwise about the origin, the new coordinates will be (-y, x).

Front

What is a reflection in geometry?

Back

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

Front

How do you reflect a point over the x-axis?

Back

To reflect a point (x, y) over the x-axis, the new coordinates will be (x, -y).

Front

How do you reflect a point over the y-axis?

Back

To reflect a point (x, y) over the y-axis, the new coordinates will be (-x, y).

Front

What is a translation in geometry?

Back

A translation is a transformation that moves a figure from one location to another without changing its shape, size, or orientation.

Front

How do you translate a point 5 units to the right?

Back

To translate a point (x, y) 5 units to the right, the new coordinates will be (x + 5, y).

Front

What is the effect of reflecting a point over the line y = x?

Back

Reflecting a point (x, y) over the line y = x results in the new coordinates (y, x).

Front

What happens to the coordinates of a point when it is reflected over the x-axis?

Back

The y-coordinate changes sign, so (x, y) becomes (x, -y).

Front

What happens to the coordinates of a point when it is reflected over the y-axis?

Back

The x-coordinate changes sign, so (x, y) becomes (-x, y).