working with sequences of transformations

Front

What is a transformation in geometry?

Back

A transformation is an operation that moves or changes a shape in some way to produce a new shape.

Front

What are the three main types of transformations?

Back

The three main types of transformations are translation, rotation, and reflection.

Front

What is a translation?

Back

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

Front

What is a reflection?

Back

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

Front

What is a rotation?

Back

A rotation is a transformation that turns a shape around a fixed point, called the center of rotation.

Front

How does reflecting a point across the y-axis affect its coordinates?

Back

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

Front

If a triangle has vertices at (2, 3), (4, 5), and (6, 7), what are the coordinates after reflecting across the x-axis?

Back

The new coordinates will be (2, -3), (4, -5), and (6, -7).

Front

What does it mean to perform a sequence of transformations?

Back

A sequence of transformations means applying multiple transformations one after the other to achieve a final position or shape.

Front

What is the result of translating a shape 3 units left?

Back

Each point of the shape will have its x-coordinate decreased by 3.

Front

How many transformations are needed to map a shape to its final position?

Back

The number of transformations needed can vary; it depends on the specific movements required.