Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure, either enlarging or reducing it, while maintaining its shape.

Front

What does the scale factor in a dilation represent?

Back

The scale factor is a number that describes how much a figure is enlarged or reduced during a dilation.

Front

If a line segment is dilated by a scale factor of 1/3, what happens to its length?

Back

The length of the line segment is reduced to one-third of its original length.

Front

What is the scale factor if a figure's length changes from 12 units to 4 units?

Back

The scale factor is 1/3.

Front

What is the result of a dilation with a scale factor greater than 1?

Back

The figure is enlarged.

Front

What is the result of a dilation with a scale factor less than 1?

Back

The figure is reduced in size.

Front

If a figure is dilated by a scale factor of 2, how does its area change?

Back

The area of the figure increases by a factor of 4 (since area scales by the square of the scale factor).

Front

True or False: A dilation can only be an enlargement.

Back

False. A dilation can be either an enlargement or a reduction.

Front

What happens to the coordinates of a point (x, y) when it is dilated by a scale factor of k?

Back

The new coordinates become (kx, ky).

Front

If a triangle has sides of lengths 3, 4, and 5, what will be the lengths of the sides after a dilation with a scale factor of 1.5?

Back

The new side lengths will be 4.5, 6, and 7.5.