Linear Transformations

Front

What is a linear transformation?

Back

A linear transformation is a function between two vector spaces that preserves the operations of vector addition and scalar multiplication.

Front

What is a translation in the context of linear transformations?

Back

A translation is a type of linear transformation that moves every point of a figure or a space by the same distance in a given direction.

Front

What does vertical stretch mean in linear transformations?

Back

A vertical stretch occurs when the y-coordinates of points are multiplied by a factor greater than 1, making the figure taller.

Front

What does vertical compression mean in linear transformations?

Back

A vertical compression occurs when the y-coordinates of points are multiplied by a factor between 0 and 1, making the figure shorter.

Front

How do you perform a translation up by 3 units?

Back

To perform a translation up by 3 units, add 3 to the y-coordinate of each point in the figure.

Front

How do you perform a translation down by 6 units?

Back

To perform a translation down by 6 units, subtract 6 from the y-coordinate of each point in the figure.

Front

How do you perform a translation left by 6 units?

Back

To perform a translation left by 6 units, subtract 6 from the x-coordinate of each point in the figure.

Front

How do you perform a translation right by 3 units?

Back

To perform a translation right by 3 units, add 3 to the x-coordinate of each point in the figure.

Front

What is the effect of a vertical stretch by a factor of 2?

Back

A vertical stretch by a factor of 2 doubles the y-coordinates of all points, making the figure twice as tall.

Front

What is the effect of a vertical compression by a factor of 0.5?

Back

A vertical compression by a factor of 0.5 halves the y-coordinates of all points, making the figure half as tall.