Transformations. Sequence of Transformations.

Front

What is a transformation in geometry?

Back

A transformation is an operation that moves or changes a shape to create a new shape. Common types include translation, rotation, reflection, and dilation.

Front

Define translation in the context of transformations.

Back

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

Front

What is a reflection in geometry?

Back

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

Front

Explain rotation in terms of transformations.

Back

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

Front

What is the difference between a rotation and a reflection?

Back

A rotation turns a shape around a point, while a reflection flips it over a line.

Front

What does it mean to map one figure onto another?

Back

To map one figure onto another means to apply a sequence of transformations that results in the second figure being congruent to the first.

Front

Describe a sequence of transformations.

Back

A sequence of transformations is a series of two or more transformations applied one after the other to achieve a final position or orientation of a shape.

Front

What is the effect of a 90° rotation counterclockwise about the origin?

Back

A 90° rotation counterclockwise about the origin moves each point of a shape to a new position that is perpendicular to its original position.

Front

How does a reflection across the x-axis affect the coordinates of a point?

Back

A reflection across the x-axis changes the sign of the y-coordinate of each point, while the x-coordinate remains the same.

Front

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

Back

The result is a new position of the shape that is first moved and then flipped over a specified line.