Solving Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that produces an image that is the same shape as the original, but is a different size. It is defined by a center point and a scale factor.

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

If a triangle has sides of lengths 3, 4, and 5, what are the side lengths after a dilation with a scale factor of 2?

Back

The new side lengths will be 6, 8, and 10.

Front

How do you find the missing side length in similar figures?

Back

To find the missing side length, set up a proportion using the corresponding sides of the similar figures and solve for the unknown.

Front

If two similar triangles have a scale factor of 3:2, and one side of the larger triangle is 12, what is the corresponding side length in the smaller triangle?

Back

The corresponding side length in the smaller triangle is 8.

Front

What is the relationship between the areas of two similar figures with a scale factor of k?

Back

The ratio of the areas of two similar figures is k², where k is the scale factor.

Front

If a rectangle has a length of 10 and a width of 5, what are the dimensions after a dilation with a scale factor of 0.5?

Back

The new dimensions will be 5 (length) and 2.5 (width).

Front

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

Back

The angles of a figure remain unchanged during a dilation.

Front

If a square has a side length of 4, what will be the side length after a dilation with a scale factor of 3?

Back

The new side length will be 12.

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.