Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that produces a figure similar to the original by increasing or decreasing its size, using a fixed point called the center of dilation and a scale factor.

Front

What is a scale factor in dilations?

Back

A 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 between 0 and 1 reduces it.

Front

If a scale factor is 1/2, what happens to the size of the figure?

Back

The figure is reduced to half its original size.

Front

True or False: A dilation always produces a congruent figure.

Back

False. A dilation produces a similar figure, not necessarily congruent.

Front

What is the center of dilation?

Back

The center of dilation is the fixed point in the plane about which all points of a figure are expanded or contracted.

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.

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 triangle is dilated by a scale factor of 1/4, what happens to its area?

Back

The area of the triangle is reduced by a factor of (1/4)² = 1/16.

Front

What is the image of point (2, 3) after a dilation with a scale factor of 2?

Back

The image is (4, 6) because each coordinate is multiplied by 2.

Front

What happens to the angles of a figure during a dilation?

Back

The angles of a figure remain unchanged during a dilation.