U9D4 Dilation

Front

What is dilation in geometry?

Back

Dilation is a transformation that alters the size of a figure but keeps its shape the same. It is defined by a center point and a scale factor.

Front

What is a scale factor in 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 shrinks it.

Front

If a point (x, y) is dilated by a scale factor of 2, what is the new point?

Back

The new point will be (2x, 2y).

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but different sizes, which means their corresponding angles are equal and their corresponding sides are proportional.

Front

What is the transformation rule for a dilation with a scale factor of 1/2?

Back

The transformation rule is (x, y) -> (0.5x, 0.5y).

Front

How do you find the scale factor when given the original and dilated points?

Back

To find the scale factor, divide the coordinates of the dilated point by the corresponding coordinates of the original point.

Front

What happens to a figure when it is dilated by a scale factor of 3/4?

Back

The figure shrinks, as the scale factor is less than 1.

Front

If point A(4, 6) is dilated to A'(2, 3), what is the scale factor?

Back

The scale factor is 0.5, since (2, 3) = (0.5 * 4, 0.5 * 6).

Front

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

Back

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

Front

What is the relationship between congruent figures and dilation?

Back

Congruent figures are identical in shape and size, meaning they can be obtained from one another through rigid transformations, not dilation.