Rigid Transformations and Their Properties

Front

What is a rigid transformation?

Back

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

Front

What is the effect of reflecting a point over the x-axis?

Back

The y-coordinate of the point changes sign, while the x-coordinate remains the same.

Front

What is the effect of reflecting a point over the y-axis?

Back

The x-coordinate of the point changes sign, while the y-coordinate remains the same.

Front

What is the rule for rotating a point 90 degrees counterclockwise around the origin?

Back

If the point is (x, y), the new coordinates will be (-y, x).

Front

What is the rule for rotating a point 180 degrees around the origin?

Back

If the point is (x, y), the new coordinates will be (-x, -y).

Front

What is the rule for rotating a point 90 degrees clockwise around the origin?

Back

If the point is (x, y), the new coordinates will be (y, -x).

Front

What is a translation in geometry?

Back

A transformation that moves every point of a figure the same distance in a given direction.

Front

What is the distance formula used for?

Back

To calculate the distance between two points (x1, y1) and (x2, y2) in a coordinate plane: d = √((x2 - x1)² + (y2 - y1)²).

Front

What is the significance of the origin in transformations?

Back

The origin (0,0) is the point around which rotations are typically performed.

Front

What happens to the coordinates of a point after a translation of (4, -2)?

Back

The new coordinates will be (x + 4, y - 2).