Dilations and Scale Factor

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but keeps its shape the same. It is defined by a center point and a scale factor.

Front

What is a scale factor?

Back

The scale factor is a number that scales, or multiplies, the dimensions of a figure during a dilation. A scale factor greater than 1 enlarges the figure, while a scale factor less than 1 reduces it.

Front

If a rectangle is dilated by a scale factor of 2, what happens to its dimensions?

Back

Each dimension of the rectangle is multiplied by 2, resulting in a rectangle that is twice as large in each direction.

Front

What does it mean if the scale factor is less than 1?

Back

If the scale factor is less than 1, the figure is reduced in size. For example, a scale factor of 1/2 means the new figure is half the size of the original.

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 point A is at (x, y) and the scale factor is k, the new coordinates A' will be (kx, ky).

Front

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

Back

A scale factor of 1 means the figure remains unchanged in size; it is neither enlarged nor reduced.

Front

If triangle ABC has vertices A(2, 3), B(4, 5), and C(6, 7), what are the coordinates after a dilation with a scale factor of 1/2?

Back

The new coordinates will be A'(1, 1.5), B'(2, 2.5), and C'(3, 3.5).

Front

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

Back

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

Front

If a figure is dilated by a scale factor of 3, what is the new area compared to the original area?

Back

The area of the dilated figure will be 3^2 = 9 times larger than the original area.

Front

What happens to the perimeter of a figure when it is dilated by a scale factor of 2?

Back

The perimeter of the figure will also double, becoming twice as long as the original perimeter.