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.

Tags

CCSS.8.G.A.3

Front

What is a scale factor in dilations?

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.

Tags

CCSS.8.G.A.3

Front

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

Back

The figure is reduced to half its original size.

Tags

CCSS.8.G.A.3

Front

How do you find the coordinates of a point after dilation?

Back

To find the coordinates of a point (x, y) after dilation with a scale factor k, multiply both coordinates by k: (kx, ky).

Tags

CCSS.8.G.A.3

Front

What are the coordinates of the image of point B (-10, -6) under a dilation with center at the origin and scale factor k = 1/2?

Back

The coordinates are (-5, -3).

Tags

CCSS.8.G.A.3

Front

What is the rule for dilating a point (x, y) by a scale factor of 2?

Back

The rule is (x, y) → (2x, 2y).

Tags

CCSS.8.G.A.3

Front

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

Back

The scale factor is 1/4.

Tags

CCSS.8.G.A.3

Front

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

Back

A negative scale factor not only changes the size of the figure but also reflects it across the center of dilation.

Tags

CCSS.8.G.A.3

Front

What happens to a triangle's area when it is dilated by a scale factor of k?

Back

The area of the triangle is multiplied by k².

Tags

CCSS.8.G.A.3

Front

If a triangle is dilated by a scale factor of 3, how does this affect the lengths of its sides?

Back

The lengths of the sides are multiplied by 3.

Tags

CCSS.8.G.A.3