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

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 are the coordinates of point C (6, -3) after a dilation with a scale factor of 2?

Back

The new coordinates will be (12, -6).

Front

How do you find the scale factor when given the original and image coordinates?

Back

The scale factor can be found by dividing the coordinates of the image by the corresponding coordinates of the original point.

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

What happens to the coordinates of a point (4, 9) under a dilation with a scale factor of 2?

Back

The new coordinates will be (8, 18).

Front

If the scale factor is 1/2, what does this indicate about the dilation?

Back

A scale factor of 1/2 indicates that the figure is being reduced to half its original size.

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

How do you determine the coordinates of the image of a point under dilation?

Back

Multiply the original coordinates of the point by the scale factor.