Unit Two: Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but preserves its shape. It is defined by a center of dilation 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 triangle ABC is dilated by a scale factor of 2, what happens to its size?

Back

The size of triangle ABC is enlarged to twice its original size.

Front

What happens to a figure when a scale factor of 0.5 is applied?

Back

The figure is reduced to half its original size.

Front

How do you determine the new coordinates of a point after dilation?

Back

To find the new coordinates after dilation, multiply the original coordinates by the scale factor.

Front

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

Back

The algebraic rule is @@(x,y) ightarrow (3x, 3y)@@.

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

Back

The algebraic rule is @@(x,y) ightarrow igg(rac{1}{4}x, rac{1}{4}yigg)@@.

Front

What does it mean for a dilation to have the origin as its center?

Back

It means that the figure is enlarged or reduced with respect to the origin point (0,0) as the reference point for the transformation.

Front

What is the result of dilating a figure by a scale factor of 0?

Back

The figure collapses to a single point at the center of dilation.