9-1 and 9-2: Dilations and Ratios 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 scale factor.

Front

What is a scale factor?

Back

A scale factor is a number that scales, or multiplies, some quantity. In dilations, it determines how much larger or smaller the image will be compared to the original.

Front

If a scale factor is greater than 1, what does that indicate about the dilation?

Back

If a scale factor is greater than 1, the dilation enlarges the original figure.

Front

If a scale factor is between 0 and 1, what does that indicate about the dilation?

Back

If a scale factor is between 0 and 1, the dilation reduces the size of the original figure.

Front

How do you calculate the scale factor when given two corresponding points?

Back

The scale factor can be calculated by dividing the distance from the center of dilation to the image point by the distance from the center of dilation to the original point.

Front

What is the relationship between the coordinates of a point and its dilated image?

Back

If a point (x, y) is dilated from the origin by a scale factor k, the coordinates of the dilated image will be (kx, ky).

Front

What is the formula for finding the scale factor when dilating a point (x, y) to (x', y')?

Back

The scale factor k can be found using the formula k = x'/x = y'/y.

Front

What does it mean for two figures to be similar?

Back

Two figures are similar if they have the same shape but not necessarily the same size, which means their corresponding angles are equal and their corresponding sides are in proportion.

Front

How can you determine if two ratios are equivalent?

Back

Two ratios are equivalent if their cross products are equal.

Front

What is a proportion in mathematics?

Back

A proportion is an equation that states that two ratios are equal.