Dilations & Similarity Test Review

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.

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.

Front

How do you calculate the coordinates of a dilated point?

Back

To calculate the coordinates of a dilated point, multiply the original coordinates by the scale factor. If the center of dilation is at the origin, the new coordinates (x', y') can be found using: x' = k * x and y' = k * y, where k is the scale factor.

Front

What happens to the coordinates of a point when a scale factor of 1 is applied?

Back

When a scale factor of 1 is applied, the coordinates of the point remain unchanged, meaning the figure does not change in size.

Front

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

Back

The new coordinates will be (kx, ky).

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.

Front

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

Back

To determine the scale factor, divide the distance from the center of dilation to the dilated point by the distance from the center of dilation to the original point.

Front

What is the relationship between similar figures and dilations?

Back

Similar figures are figures that have the same shape but may have different sizes. Dilation is the transformation that creates similar figures by enlarging or reducing the original figure.

Front

How do you perform a dilation with a center not at the origin?

Back

To perform a dilation with a center not at the origin, first translate the figure so that the center of dilation is at the origin, perform the dilation, and then translate the figure back to its original position.

Front

What is the formula for dilating a point (x, y) with a center of dilation (h, k) and a scale factor of k?

Back

The formula is: x' = h + k(x - h) and y' = k + k(y - k).