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 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 find the image of a point under dilation with a scale factor?

Back

To find the image of a point (x, y) under dilation with a scale factor r, multiply both coordinates by r: (rx, ry).

Front

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

Back

When the scale factor is 1, the coordinates of the point remain unchanged; the image is the same as the original.

Front

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

Back

The new coordinates will be (2x, 2y).

Front

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

Back

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

Front

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

Back

To determine the scale factor, divide the coordinates of the dilated point by the corresponding coordinates of the original point.

Front

What is the coordinate of the image of the point (4, 9) under a dilation with a scale factor of 2?

Back

The coordinate of the image is (8, 18).

Front

What is the coordinate of the image of the point (-10, -6) under a dilation with a scale factor of 1/2?

Back

The coordinate of the image is (-5, -3).

Front

True or False: A dilation with a scale factor of 1/4 is an enlargement.

Back

False, it is a reduction.