Dilations & Similar Figures

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 is defined by a center point and a scale factor.

Front

What is the scale factor in a 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 AB is dilated by a scale factor of 3 to produce A'B', and A'B' = 6, what is AB?

Back

AB = 2.

Front

If AB = 7 and A'B' = 21, what is the scale factor?

Back

The scale factor is 3.

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but not necessarily the same size. This means their corresponding angles are equal and their corresponding sides are in proportion.

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 image by the length of the corresponding side of the original figure.

Front

Which scale factor would create a larger image: 8, 1/8, or -300?

Back

The scale factor 8 would create a larger image.

Front

What is the relationship between the sides of similar figures?

Back

The ratios of the lengths of corresponding sides of similar figures are equal to the scale factor.

Front

If the scale factor is 2, what happens to the area of the figure?

Back

If the scale factor is 2, the area of the figure increases by a factor of 2^2 = 4.

Front

What is the formula for the area of similar figures in relation to the scale factor?

Back

If the scale factor is k, then the ratio of the areas of two similar figures is k^2.