Dilations

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 the 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 point B (4,9) is dilated with a scale factor of 2, what are the coordinates of the image?

Back

(8,18)

Front

What happens to the coordinates of a point when it undergoes a dilation with a scale factor of r?

Back

The new coordinates (x', y') are found by multiplying the original coordinates (x, y) by the scale factor r: (x', y') = (r*x, r*y).

Front

Is a dilation always a congruence transformation?

Back

No, a dilation is not a congruence transformation because it does not preserve size; it changes the size of the figure.

Front

What is the center of dilation?

Back

The center of dilation is the fixed point in the plane about which all points are expanded or contracted during the dilation.

Front

If the scale factor is 1/2, what happens to the size of the figure?

Back

The figure is reduced to half its original size.

Front

How do you determine if a dilation enlarges or reduces a figure?

Back

If the scale factor is greater than 1, the figure enlarges. If the scale factor is between 0 and 1, the figure reduces.

Front

What is the effect of a negative scale factor in a dilation?

Back

A negative scale factor not only changes the size of the figure but also reflects it across the center of dilation.

Front

If a dilation has a center at the origin and a scale factor of 3, what are the new coordinates of point (2,5)?

Back

(6,15)