Rigid Transformations

Front

What is a rigid transformation?

Back

A rigid transformation is a transformation that preserves the shape and size of a figure. The three types of rigid transformations are translations, rotations, and reflections.

Front

Define translation in geometry.

Back

Translation is a type of rigid transformation that slides a figure from one position to another without turning it. It is defined by a vector that indicates the direction and distance of the slide.

Front

What does it mean to reflect a point over the y-axis?

Back

Reflecting a point over the y-axis means to create a mirror image of the point across the y-axis. For a point (x, y), the reflected point is (-x, y).

Front

How do you perform a 90° clockwise rotation about the origin?

Back

To perform a 90° clockwise rotation about the origin, you switch the coordinates of the point (x, y) to (y, -x).

Front

What are the coordinates of point A after translating (2, 3) right 4 and down 2?

Back

The new coordinates of point A are (6, 1).

Front

Explain what a reflection across the line x = -2 means.

Back

A reflection across the line x = -2 means that each point is mirrored over the vertical line x = -2. For a point (x, y), the reflected point is (-4 - x, y).

Front

What is the result of translating the point (1, -1) left 3 and up 2?

Back

The new coordinates are (-2, 1).

Front

Describe the transformation: moving a shape 5 units to the left and 3 units up.

Back

This transformation is a translation defined by the vector (-5, 3).

Front

What happens to the coordinates of a point when it is reflected over the x-axis?

Back

When a point (x, y) is reflected over the x-axis, the new coordinates become (x, -y).

Front

If a triangle is rotated 180° about the origin, what happens to its vertices?

Back

Each vertex (x, y) of the triangle will move to the position (-x, -y).