Translations, Reflections, and Rotations

Front

What is a translation in geometry?

Back

A translation is a transformation that moves every point of a shape a constant distance in a specified direction.

Front

How do you find the new coordinates after a translation?

Back

To find the new coordinates after a translation, add the translation values to the original coordinates. For example, translating point (x, y) by (a, b) results in (x+a, y+b).

Front

What is a reflection in geometry?

Back

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

Front

What is a rotation in geometry?

Back

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

Front

What are the coordinates of a point after a 180° rotation around the origin?

Back

The coordinates (x, y) become (-x, -y) after a 180° rotation around the origin.

Front

What happens to the length of a segment during a rotation?

Back

The length of a segment remains the same during a rotation.

Front

If a shape is translated 8 units right and 2 units down, what is the transformation rule?

Back

The transformation rule is (x, y) → (x+8, y-2).

Front

What is the effect of a 90° clockwise rotation on the coordinates (x, y)?

Back

The coordinates (x, y) become (y, -x) after a 90° clockwise rotation.

Front

What is the effect of a 90° counterclockwise rotation on the coordinates (x, y)?

Back

The coordinates (x, y) become (-y, x) after a 90° counterclockwise rotation.

Front

What is the difference between a translation and a rotation?

Back

A translation moves a shape without changing its orientation, while a rotation turns a shape around a point.