Dilations Practice

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 scale factor.

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. In dilations, it determines how much larger or smaller the image will be compared to the original shape.

Front

If a shape is dilated by a scale factor of k, how do the lengths of the sides of the shape change?

Back

The lengths of the sides of the shape are multiplied by the scale factor k.

Front

What happens to the perimeter of a shape when it is dilated by a scale factor of 3?

Back

The new perimeter is 3 times the original perimeter.

Front

If a triangle has sides of lengths 3, 4, and 5, and is dilated by a scale factor of 2, what are the lengths of the sides of the new triangle?

Back

The new triangle will have sides of lengths 6, 8, and 10.

Front

What is the effect of a scale factor less than 1 on a shape?

Back

A scale factor less than 1 reduces the size of the shape.

Front

What is the effect of a negative scale factor on a shape?

Back

A negative scale factor not only changes the size of the shape but also reflects it across the origin.

Front

If a triangle ABC is dilated to form triangle A'B'C' with a scale factor of 1/2, what is the relationship between the sides of the two triangles?

Back

The sides of triangle A'B'C' will be half the lengths of the corresponding sides of triangle ABC.

Front

How do you determine the scale factor when given the lengths of corresponding sides of two similar shapes?

Back

The scale factor can be determined by dividing the length of a side of the image by the length of the corresponding side of the original shape.

Front

What is the relationship between the areas of two similar shapes when one is a dilation of the other?

Back

The area of the dilated shape is equal to the area of the original shape multiplied by the square of the scale factor.