Geometry | Unit 5 | Lesson 3: Creating Cross Sections by Dilating | Practice Problems

Front

What is a dilation in geometry?

Back

A dilation is a transformation that alters the size of a figure but maintains its shape, using a center point and a scale factor.

Front

What is a scale factor in the context of dilations?

Back

A 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 determine the scale factor when dilating a figure?

Back

The scale factor can be determined by comparing the lengths of corresponding sides of the original figure and the dilated figure.

Front

What does it mean for cross sections to be dilations of a figure?

Back

It means that the cross sections are similar to the original figure but scaled up or down based on a specific scale factor.

Front

What is the significance of the center of dilation?

Back

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

Front

How can you find the horizontal cross sections of a three-dimensional figure?

Back

Horizontal cross sections can be found by slicing the figure parallel to the base, which reveals the shape of the figure at that height.

Front

What is the relationship between the scale factors of cross sections and the original figure?

Back

The scale factors of the cross sections are proportional to the distances from the center of dilation to the points on the original figure.

Front

What is the formula for calculating the area of a dilated figure?

Back

The area of a dilated figure can be calculated using the formula: Area' = (scale factor)^2 * Area, where Area' is the area of the dilated figure.

Front

How does the scale factor affect the perimeter of a dilated figure?

Back

The perimeter of a dilated figure is affected by the scale factor in a linear manner: Perimeter' = scale factor * Perimeter.

Front

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

Back

A scale factor of 1 means that the figure remains unchanged in size; it is congruent to the original figure.