Dilations and Scale Factor

Front

What is a dilation in geometry?

Back

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. It involves a center of dilation and a scale factor.

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. In dilations, it determines how much larger or smaller the image will be compared to the original figure.

Front

If the scale factor is greater than 1, what type of transformation occurs?

Back

An enlargement occurs when the scale factor is greater than 1.

Front

If the scale factor is less than 1, what type of transformation occurs?

Back

A reduction occurs when the scale factor is less than 1.

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

True or False: A dilation produces congruent figures.

Back

False. A dilation produces similar figures, not congruent figures.

Front

What is the center of dilation?

Back

The center of dilation is a fixed point in the plane about which all points are expanded or contracted.

Front

How do you determine if a dilation is an enlargement or a reduction?

Back

If the scale factor is greater than 1, it is an enlargement; if it is less than 1, it is a reduction.

Front

What is the scale factor if a point (4, 6) is dilated to (2, 3)?

Back

The scale factor is 1/2.

Front

If a figure is dilated by a scale factor of 3, what happens to its area?

Back

The area of the figure is multiplied by the square of the scale factor, so it becomes 9 times larger.