Rigid Motions

Front

What is a rigid motion in geometry?

Back

A rigid motion is a transformation that preserves the shape and size of a figure, meaning the figure's dimensions and angles remain unchanged.

Front

What are the three main types of rigid motions?

Back

The three main types of rigid motions are translations, rotations, and reflections.

Front

How do you describe a translation in coordinate geometry?

Back

A translation is described by a rule that indicates how each point of a figure moves in the coordinate plane, typically in the form (x + a, y + b), where 'a' and 'b' are the horizontal and vertical shifts, respectively.

Front

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

Back

The rule for rotating a point (x, y) 90° counterclockwise around the origin is (x, y) → (-y, x).

Front

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

Back

The rule for rotating a point (x, y) 180° around the origin is (x, y) → (-x, -y).

Front

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

Back

The rule for rotating a point (x, y) 270° counterclockwise around the origin is (x, y) → (y, -x).

Front

What does a reflection across the x-axis do to a point (x, y)?

Back

A reflection across the x-axis transforms the point (x, y) to (x, -y).

Front

What does a reflection across the y-axis do to a point (x, y)?

Back

A reflection across the y-axis transforms the point (x, y) to (-x, y).

Front

How can you determine the new location of a triangle after a rotation?

Back

To determine the new location of a triangle after a rotation, apply the appropriate rotation rule to each vertex of the triangle.

Front

What is the effect of a translation on the coordinates of a figure?

Back

A translation shifts the entire figure by a specified distance in a specified direction without changing its shape or orientation.