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, called the image.

Front

What are the four main types of transformations?

Back

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

Front

What is a dilation in geometry?

Back

A dilation is a transformation that changes the size of a figure but not its shape, using a scale factor.

Front

What does the scale factor in a dilation represent?

Back

The scale factor represents how much the figure is enlarged or reduced. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

If a point (x, y) is dilated by a scale factor k, what is the new coordinate?

Back

The new coordinate is (kx, ky).

Front

What happens to a shape when it is translated?

Back

When a shape is translated, it moves from one location to another without changing its size, shape, or orientation.

Front

In a translation, what does the notation (x, y + 6) indicate?

Back

It indicates that the shape moves 6 units up on the y-axis.

Front

What is the effect of a reflection over the x-axis on a point (x, y)?

Back

The effect of a reflection over the x-axis on a point (x, y) is to produce the point (x, -y).

Front

What is the effect of a rotation of 90 degrees counterclockwise on a point (x, y)?

Back

The effect of a rotation of 90 degrees counterclockwise on a point (x, y) is to produce the point (-y, x).

Front

What is the difference between a reduction and an enlargement in dilation?

Back

A reduction occurs when the scale factor is between 0 and 1, making the image smaller, while an enlargement occurs when the scale factor is greater than 1, making the image larger.