13.2 Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but not its shape, using a center of dilation 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.

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 greater than 1?

Back

The coordinates of the point will increase, making the figure larger.

Front

What happens to the coordinates of a point when it is dilated by a scale factor between 0 and 1?

Back

The coordinates of the point will decrease, making the figure smaller.

Front

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

Back

Divide the coordinates of the dilated point by the corresponding coordinates of the original point.

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 a figure is dilated by a scale factor of 2, what does this mean?

Back

It means that every point of the figure moves away from the center of dilation, doubling its distance from that point.

Front

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

Back

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

Front

How do you dilate a figure with respect to a point other than the origin?

Back

To dilate with respect to a point other than the origin, translate the figure so that the center of dilation is at the origin, perform the dilation, and then translate back.