compositions of transformations

Front

What is a transformation in geometry?

Back

A transformation in geometry is an operation that moves or changes a shape in some way to produce a new shape.

Front

What are the four main types of transformations?

Back

The four main types of transformations are translation, rotation, reflection, and dilation.

Front

Define translation in geometry.

Back

Translation is a transformation that moves every point of a shape the same distance in the same direction.

Front

What is a rotation?

Back

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

Front

Explain reflection in geometry.

Back

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

Front

What is the effect of a 90-degree rotation on a point (x, y)?

Back

A 90-degree rotation counterclockwise around the origin transforms the point (x, y) to (-y, x).

Front

What happens to a shape during a reflection over the x-axis?

Back

During a reflection over the x-axis, the y-coordinates of the points of the shape change sign, transforming (x, y) to (x, -y).

Front

What is the result of a reflection followed by a rotation?

Back

The result of a reflection followed by a rotation is a new position of the shape that depends on the order and angle of the rotation.

Front

How does a composition of transformations work?

Back

A composition of transformations involves applying two or more transformations in sequence to a shape.

Front

What is the difference between a rigid transformation and a non-rigid transformation?

Back

A rigid transformation preserves the shape and size of a figure, while a non-rigid transformation may change the size or shape.