Dilations & Similar Figures

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but maintains its shape. 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 a figure is dilated by a scale factor of 3, what happens to its dimensions?

Back

All dimensions of the figure are multiplied by 3, making the figure three times larger.

Front

How do you find the scale factor when given the original and dilated lengths?

Back

The scale factor can be found by dividing the length of the dilated figure by the length of the original figure: Scale Factor = \( \frac{Length_{dilated}}{Length_{original}} \).

Front

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

Back

The scale factor is 3.

Front

Which scale factor would create a larger image: -300, 8, 1/8, or 1/100?

Back

The scale factor 8 would create a larger image.

Front

If A'B' = 6 and the scale factor is 3, what is AB?

Back

AB = 2.

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. Their corresponding angles are equal, and their corresponding sides are proportional.

Front

How do you set up a proportion for similar figures?

Back

To set up a proportion, compare the lengths of corresponding sides of the similar figures. For example, if two triangles are similar, you can write \( \frac{a}{b} = \frac{c}{d} \) where a and b are sides of one triangle and c and d are sides of the other.

Front

What is the relationship between the scale factor and the areas of similar figures?

Back

The ratio of the areas of two similar figures is equal to the square of the scale factor. If the scale factor is k, then the area ratio is k^2.