Geometry: Rigid Transformations Flashcard

Front

What is a rigid transformation in geometry?

Back

A rigid transformation is a transformation that preserves the shape and size of a figure, including translations, rotations, and reflections.

Front

How do you perform a translation of a point in the coordinate plane?

Back

To translate a point, you add the translation vector's x-component to the x-coordinate and the y-component to the y-coordinate of the point.

Front

What is the result of a transformation called?

Back

The result of a transformation is called the image.

Front

What is the angle of rotation for a 90° counterclockwise rotation about the origin?

Back

The angle of rotation is 90°.

Front

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

Back

To reflect a point (x, y) across the x-axis, you change the sign of the y-coordinate, resulting in the point (x, -y).

Front

What are the coordinates of a point after a translation of 3 units left and 9 units down from (1, 4)?

Back

The new coordinates would be (-2, -5).

Front

What is the effect of a 180° rotation about the origin on the point (x, y)?

Back

A 180° rotation about the origin transforms the point (x, y) to (-x, -y).

Front

What does a reflection across the y-axis do to the coordinates of a point?

Back

A reflection across the y-axis changes the sign of the x-coordinate, resulting in the point (-x, y).

Front

If a point is rotated 270° counterclockwise about the origin, what is the equivalent clockwise rotation?

Back

The equivalent clockwise rotation is 90°.

Front

What is the general formula for translating a point (x, y) by a vector (a, b)?

Back

The new coordinates after translation are (x + a, y + b).