Dilations: Writing the Rule

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but not its shape, using a center point and a scale factor.

Front

What is a scale factor in dilations?

Back

The scale factor is a number that scales, or multiplies, the dimensions of a figure during a dilation. A scale factor greater than 1 enlarges the figure, while a scale factor between 0 and 1 reduces it.

Front

How do you represent a dilation algebraically?

Back

A dilation can be represented as (x, y) → (kx, ky), where k is the scale factor.

Front

If the scale factor is 2, what is the dilation of the point (3, 4)?

Back

The dilation of the point (3, 4) with a scale factor of 2 is (6, 8).

Front

If the scale factor is 0.5, what happens to the figure?

Back

If the scale factor is 0.5, the figure is reduced to half its original size.

Front

What is the effect of a scale factor of 1 on a figure?

Back

A scale factor of 1 means the figure remains the same size; it is unchanged.

Front

How do you find the center of dilation?

Back

The center of dilation is the fixed point in the plane about which all points are expanded or contracted.

Front

What is the difference between enlargement and reduction in dilations?

Back

Enlargement occurs when the scale factor is greater than 1, while reduction occurs when the scale factor is between 0 and 1.

Front

What is the algebraic representation of a dilation with a scale factor of 3?

Back

The algebraic representation is (x, y) → (3x, 3y).

Front

How can you determine if a transformation is a dilation?

Back

A transformation is a dilation if it maintains the shape of the figure but changes its size, and all points move away from or towards a center point.