Dilations and Scale Factors

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but preserves its shape. It is defined by a center point and a scale factor.

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, the dimensions of a figure. A scale factor greater than 1 enlarges the figure, while a scale factor less than 1 shrinks it.

Front

If a candy rope is 12 inches long and is dilated by a scale factor of 1/4, what is the new length?

Back

3 inches

Front

What happens to a figure when the scale factor is greater than 1?

Back

The figure enlarges (grows).

Front

If a candy rope is 12 inches long and is dilated by a scale factor of 3, what is the new length?

Back

36 inches

Front

What does a scale factor of 1 indicate?

Back

A scale factor of 1 means the figure remains the same size (it is preserved).

Front

How do you find the scale factor between two similar figures?

Back

To find the scale factor, divide the length of a side of the larger figure by the corresponding side of the smaller figure.

Front

If a TV measures 7 inches by 9 inches and is replaced by a TV measuring 56 inches by 72 inches, what is the scale factor?

Back

8

Front

What is the effect of a scale factor less than 1 on a figure?

Back

A scale factor less than 1 reduces (shrinks) the figure.

Front

If a figure is dilated by a scale factor of 1/2, what happens to its area?

Back

The area of the figure is reduced to 1/4 of its original area.