Composition of Rigid Transformations

Front

What is the composition of transformations?

Back

A transformation in which a second transformation is performed on the image of a first transformation.

Front

What are rigid transformations?

Back

Transformations that preserve distance and angle, including translations, rotations, and reflections.

Front

What is a translation in geometry?

Back

A transformation that moves every point of a figure the same distance in the same direction.

Front

What is a reflection in geometry?

Back

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

Front

What is a rotation in geometry?

Back

A transformation that turns a figure around a fixed point at a certain angle.

Front

How do you perform a translation on a point?

Back

Add the translation vector to the coordinates of the point.

Front

What is the effect of reflecting a point over the x-axis?

Back

The y-coordinate of the point changes sign, while the x-coordinate remains the same.

Front

What is the effect of rotating a point 90 degrees counterclockwise around the origin?

Back

The new coordinates (x, y) become (-y, x).

Front

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

Back

The final position of the figure depends on the order and type of transformations applied.

Front

What is the notation for a translation of a point (x, y) by (a, b)?

Back

T(a, b)(x, y) = (x + a, y + b).