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 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 point (x, y) is dilated by a scale factor of k, what are the new coordinates?

Back

The new coordinates will be (kx, ky).

Front

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

Back

The coordinates remain unchanged; the point does not move.

Front

What is the effect of a scale factor less than 1 on a geometric figure?

Back

A scale factor less than 1 results in a reduction of the figure, making it smaller.

Front

How do you determine the coordinates of a dilated point given a scale factor?

Back

Multiply each coordinate of the original point by the scale factor.

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.

Front

If Triangle ABC is dilated by a scale factor of 2, what happens to its area?

Back

The area of Triangle ABC will be multiplied by the square of the scale factor, so it will increase by a factor of 4.

Front

What is the relationship between the scale factor and the size of the image produced by a dilation?

Back

The size of the image is directly proportional to the scale factor; larger scale factors produce larger images.

Front

How do you express a dilation transformation mathematically?

Back

A dilation transformation can be expressed as (x, y) → (kx, ky), where k is the scale factor.