Dilations and Sequences

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but keeps its shape the same, using a center of dilation and a scale factor.

Front

What does the scale factor in a dilation represent?

Back

The scale factor indicates how much the figure is enlarged or reduced. 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 2, what happens to its dimensions?

Back

Each dimension of the figure is multiplied by 2, resulting in a figure that is twice as large.

Front

What is the center of dilation?

Back

The center of dilation is a fixed point in the plane about which the figure is enlarged or reduced.

Front

How do you find the coordinates of a dilated point?

Back

To find the coordinates of a dilated point, multiply the original coordinates by the scale factor.

Front

What is the result of dilating a point (x, y) by a scale factor of 1?

Back

The result is the same point (x, y), as the figure does not change size.

Front

What happens to a figure when it is dilated by a scale factor of 1/2?

Back

The figure is reduced to half its original size, maintaining its shape.

Front

What is the relationship between dilations and similar figures?

Back

Dilations produce similar figures, meaning they have the same shape but different sizes.

Front

If point (4, 6) is dilated by a scale factor of 3, what are the new coordinates?

Back

The new coordinates are (12, 18), calculated by multiplying each coordinate by 3.

Front

True or False: A dilation can change the angles of a figure.

Back

False. A dilation does not change the angles; it only changes the size.