Rigid Transformations

Front

What is a rigid transformation?

Back

A rigid transformation is a transformation that preserves the shape and size of a figure. Examples include translations, rotations, and reflections.

Front

What is translation in geometry?

Back

Translation is a type of transformation that moves every point of a figure the same distance in a specified direction.

Front

How do you perform a translation of a point?

Back

To translate a point, you add the translation vector to the coordinates of the point. For example, to translate point (x, y) by (a, b), the new point will be (x+a, y+b).

Front

What is the result of translating the point (2, 3) by 5 units left and 2 units up?

Back

The new coordinates will be (-3, 5).

Front

What is a reflection in geometry?

Back

A reflection is a transformation that flips a figure over a line, creating a mirror image.

Front

What is the line of reflection?

Back

The line of reflection is the line over which a figure is reflected. Points on the figure are equidistant from this line.

Front

What is a rotation in geometry?

Back

A rotation is a transformation that turns a figure around a fixed point, known as the center of rotation, by a certain angle.

Front

What does it mean to rotate a figure 90 degrees counterclockwise?

Back

To rotate a figure 90 degrees counterclockwise means to turn the figure 90 degrees in the opposite direction of the clock's hands around a specified point.

Front

What are congruent figures?

Back

Congruent figures are figures that have the same shape and size, and can be obtained from one another through rigid transformations.

Front

What is the difference between a translation and a reflection?

Back

A translation moves a figure without changing its orientation, while a reflection flips a figure over a line, changing its orientation.