Dilations on the Coordinate Plane

Front

What is a dilation in geometry?

Back

A dilation is a transformation that changes the size of a figure but not its shape, using a scale factor.

Tags

CCSS.8.G.A.3

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 between 0 and 1 reduces it.

Tags

CCSS.8.G.A.3

Front

What is the effect of a scale factor of 1 in a dilation?

Back

A scale factor of 1 means the figure remains unchanged in size.

Tags

CCSS.8.G.A.3

Front

What is the rule for a dilation with a scale factor of 2?

Back

The rule is (x, y) → (2x, 2y), meaning each coordinate is multiplied by 2.

Tags

CCSS.8.G.A.3

Front

What is the rule for a dilation with a scale factor of 1/3?

Back

The rule is (x, y) → (1/3x, 1/3y), meaning each coordinate is multiplied by 1/3.

Tags

CCSS.8.G.A.3

Front

Which point remains unchanged after a dilation?

Back

The center of dilation remains unchanged; all other points change based on the scale factor.

Tags

CCSS.8.G.A.3

Front

If a rectangle is dilated by a scale factor of 2, what happens to its area?

Back

The area of the rectangle increases by a factor of 2² = 4.

Tags

CCSS.7.G.A.1

Front

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

Back

Multiply the original coordinates by the scale factor. For example, if the point is (x, y) and the scale factor is k, the new coordinates are (kx, ky).

Tags

CCSS.8.G.A.3

Front

What happens to the distances between points after a dilation?

Back

The distances between points are multiplied by the scale factor.

Tags

CCSS.8.G.A.3

Front

If a figure is dilated by a scale factor of 1/2, what happens to its perimeter?

Back

The perimeter of the figure is reduced by a factor of 1/2.

Tags

CCSS.8.G.A.3