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 of dilation and a scale factor.

Front

What is the center of dilation?

Back

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

Front

What is a scale factor in dilation?

Back

The scale factor (k) is a number that describes how much a figure is enlarged or reduced during a dilation. If k > 1, the figure is enlarged; if 0 < k < 1, the figure is reduced.

Front

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

Back

The new coordinates are (8, 12).

Front

If the point (2, 3) is dilated with a scale factor of ½, what are the new coordinates?

Back

The new coordinates are (1, 1.5).

Front

True or False: A dilation produces a congruent figure.

Back

False. A dilation produces a similar figure, not a congruent figure.

Front

What happens to the distances between points during a dilation?

Back

The distances between points are multiplied by the scale factor.

Front

If a figure is dilated by a scale factor of 1, what happens to the figure?

Back

The figure remains unchanged.

Front

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

Back

A negative scale factor reflects the figure across the center of dilation and changes its size.

Front

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

Back

The scale factor (k) can be found by dividing the distance from the center of dilation to the dilated point by the distance from the center of dilation to the original point.