Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that changes the size of a figure but not its shape. It involves a scale factor and a center of dilation.

Front

What is a scale factor in dilation?

Back

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

Front

If a figure is dilated by a scale factor of 2, what happens to its dimensions?

Back

Each dimension of the figure is multiplied by 2, making the figure twice as large.

Front

What happens to the coordinates of a point (x, y) when it is dilated by a scale factor of k?

Back

The new coordinates will be (kx, ky).

Front

What is the dilation rule for a scale factor of 1/2?

Back

The dilation rule is (x, y) → (1/2 x, 1/2 y), which reduces the size of the figure by half.

Front

How do you determine the center of dilation?

Back

The center of dilation is a fixed point in the plane from which all points are expanded or contracted. It can be any point, not necessarily on the figure.

Front

What is the effect of a negative scale factor in dilation?

Back

A negative scale factor not only changes the size of the figure but also reflects it across the center of dilation.

Front

If a rectangle is dilated and the coordinates of one vertex change from (2, 3) to (4, 6), what is the scale factor?

Back

The scale factor is 2, since both coordinates are multiplied by 2.

Front

What is the difference between enlargement and reduction in dilation?

Back

Enlargement occurs when the scale factor is greater than 1, while reduction occurs when the scale factor is between 0 and 1.

Front

How can you identify a dilation from a set of coordinates?

Back

You can identify a dilation by checking if the coordinates of the new figure are proportional to the original figure's coordinates based on a consistent scale factor.