Compose 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 main types of transformations?

Back

The main types of transformations are translations, rotations, reflections, and dilations.

Front

Define translation in the context of transformations.

Back

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

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

Explain reflection in geometric transformations.

Back

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

Front

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

Back

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

Front

How does a translation of 3 units left and 2 units down affect the point (5, 4)?

Back

The point (5, 4) would be transformed to (5 - 3, 4 - 2) = (2, 2).

Front

What is the result of reflecting a point (x, y) across the x-axis?

Back

Reflecting a point (x, y) across the x-axis results in the point (x, -y).

Front

Describe the sequence of transformations that maps Triangle ABC to Triangle A'B'C'.

Back

The sequence may include a combination of translations, rotations, and reflections, depending on the specific positions of the triangles.

Front

What is the difference between rigid motions and non-rigid motions?

Back

Rigid motions preserve the shape and size of a figure (translations, rotations, reflections), while non-rigid motions can change the size or shape (like dilations).