Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but keeps its shape, using a scale factor.

Front

What does the scale factor in a dilation represent?

Back

The scale factor indicates how much the figure is enlarged or reduced. A scale factor greater than 1 enlarges the figure, while a scale factor less than 1 reduces it.

Front

If the point (8, 12) is dilated to (2, 3), what is the scale factor?

Back

1/4

Front

True or False: A dilation with a scale factor greater than 1 results in an enlargement.

Back

True

Front

True or False: A dilation with a scale factor less than 1 results in a reduction.

Back

True

Front

What is the result of a dilation on a figure?

Back

A dilation produces a similar figure, meaning the new figure has the same shape but a different size.

Front

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

Back

(2, 4), (6, 8), (10, 12) - each coordinate is multiplied by 2.

Front

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

Back

The angles remain unchanged during a dilation.

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 square with a side length of 4 is dilated by a scale factor of 1/2, what is the new side length?

Back

2 - the new side length is 4 multiplied by 1/2.