Dilations

Front

What is a dilation in geometry?

Back

A dilation is a transformation that produces a figure similar to the original by enlarging or reducing it, using 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 indicates enlargement, while a scale factor between 0 and 1 indicates reduction.

Front

If a figure is dilated by a scale factor of 3, what happens to its dimensions?

Back

All dimensions of the figure are multiplied by 3, making the figure three times larger.

Front

How do you find the coordinates of a dilated point?

Back

To find the coordinates of a dilated point, multiply the original coordinates by the scale factor.

Front

What are similar figures?

Back

Similar figures are figures that have the same shape but may differ in size. They have proportional corresponding sides and equal corresponding angles.

Front

What is the center of dilation?

Back

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

Front

If triangle ABC has vertices A(2,3), B(4,5), and C(6,7), what are the coordinates after a dilation by a scale factor of 2?

Back

A'(4,6), B'(8,10), C'(12,14) - each coordinate is multiplied by 2.

Front

What does it mean to reduce a figure?

Back

To reduce a figure means to make it smaller by applying a scale factor less than 1 during a dilation.

Front

What is the relationship between the original figure and its dilated image?

Back

The original figure and its dilated image are similar, meaning they have the same shape but different sizes.

Front

If a window in a model is 1.5 in. wide and the scale is 5 in:25 ft, how wide is the actual window?

Back

The actual window is 7.5 ft wide.