Topic 7: Dilations and Similarity II

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but not its shape, using 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.

Front

If a figure is dilated by a scale factor greater than 1, what happens to its size?

Back

The figure becomes larger.

Front

If a figure is dilated by a scale factor less than 1, what happens to its size?

Back

The figure becomes smaller.

Front

How do you find the coordinates of a dilated point?

Back

Multiply the original coordinates by the scale factor.

Front

What is the algebraic rule for dilating a point (x, y) by a scale factor of k?

Back

(x, y) --> (kx, ky) where k is the scale factor.

Front

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

Back

The scale factor is 1/2.

Front

What happens to the area of a figure when it is dilated by a scale factor of k?

Back

The area is multiplied by k².

Front

If a rectangle has dimensions 4 ft by 6 ft and is dilated by a scale factor of 3, what are the new dimensions?

Back

The new dimensions are 12 ft by 18 ft.

Front

What is the relationship between the lengths of corresponding sides of similar figures?

Back

The lengths of corresponding sides are proportional to the scale factor.