Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that changes the size of a figure but not its shape. It involves a scale factor and a center of dilation.

Front

What does the scale factor in a dilation represent?

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

How do you dilate a point (x, y) by a scale factor k over the origin?

Back

To dilate a point (x, y) by a scale factor k over the origin, multiply both coordinates by k: (kx, ky).

Front

If the point (4, 6) is dilated by a scale factor of 2, what are the new coordinates?

Back

(8, 12) - The coordinates are multiplied by 2.

Front

What happens to the coordinates of a point when it is dilated by a scale factor of 1?

Back

The coordinates remain the same; the point does not change.

Front

If a point (a, b) is dilated by a scale factor of 1/2, what are the new coordinates?

Back

(a/2, b/2) - Each coordinate is halved.

Front

What is the relationship between similar figures and dilations?

Back

Dilations create similar figures; the shapes are proportional but not necessarily congruent.

Front

How can you determine if a transformation is a dilation?

Back

Check if the figures are similar and if the distances between corresponding points are proportional.

Front

What is the scale factor if the point (3, 4) is dilated to (6, 8)?

Back

The scale factor is 2, as each coordinate is multiplied by 2.

Front

If a figure is dilated by a scale factor of 1/3, how does its area change?

Back

The area of the figure is reduced by a factor of (1/3)^2 = 1/9.