Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that changes the size of a figure but not its shape. It involves a scale factor and a center of dilation.

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 coordinates of a dilated point?

Back

To find the coordinates of a dilated point, multiply the original coordinates by the scale factor. For example, if the original point is (x, y) and the scale factor is k, 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

When a point is dilated by a scale factor of 1, its coordinates remain unchanged.

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

If a triangle has vertices at (2, 3), (4, 5), and (6, 1), what are the new coordinates after a dilation by a scale factor of 2?

Back

The new coordinates will be (4, 6), (8, 10), and (12, 2).

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

If a figure is dilated by a scale factor of 1/2, what happens to its area?

Back

The area of the figure is reduced by a factor of (1/2)² = 1/4.

Front

What is the relationship between the original figure and the dilated figure?

Back

The dilated figure is similar to the original figure, meaning they have the same shape but different sizes.

Front

How do you determine if two figures are similar?

Back

Two figures are similar if their corresponding angles are equal and the lengths of their corresponding sides are proportional.