Understanding Dilations and Scale Factors

This video tutorial covers Module 3 Lesson 2, focusing on the fundamental theorem of similarity. It explores the effects of dilations, translations, rotations, and reflections on two-dimensional figures. The lesson includes calculating scale factors, plotting dilations on coordinate grids, and understanding the relationship between scale factors and perimeters. Through examples, students learn to identify parallel segments and congruent angles, and practice graphing dilations to reinforce their understanding.

What is the primary focus of the fundamental theorem of similarity discussed in the lesson?

• Effects of rotations on three-dimensional figures

• Effects of translations on two-dimensional figures

• Effects of dilations on two-dimensional figures

• Effects of dilations on three-dimensional figures

If a segment is dilated with a scale factor of 3, what happens to its length?

• It triples in length

• It remains the same

• It becomes one-third of the original length

• It doubles in length

How do you determine the scale factor when given the lengths of the image and pre-image?

• Divide the length of the pre-image by the image

• Subtract the length of the pre-image from the image

• Multiply the lengths of the image and pre-image

• Divide the length of the image by the pre-image

What is the effect of a scale factor less than one on a figure?

• It keeps the figure the same size

• It rotates the figure

• It reduces the figure

• It enlarges the figure

When a triangle's perimeter is doubled, what can be inferred about the scale factor?

• The scale factor is 0.5

• The scale factor is 1

• The scale factor is 2

• The scale factor is 3

How does the perimeter of a dilated triangle compare to its original when the scale factor is 2?

• The perimeter is halved

• The perimeter is doubled

• The perimeter is tripled

• The perimeter remains the same

What happens to the coordinates of a point when it is dilated by a scale factor of 2?

• Each coordinate is halved

• Each coordinate is doubled

• Each coordinate is tripled

• Each coordinate remains the same

If a point is at (3, 4) and is dilated by a scale factor of 0.5, where will it be located?

• (3, 4)

• (0, 0)

• (1.5, 2)

• (6, 8)

What is the result of dilating a figure by a scale factor of 1?

• The figure is enlarged

• The figure is reduced

• The figure is rotated

• The figure remains unchanged

In graphing dilated figures, what is the first step?

• Plot the image first

• Plot the pre-image first

• Calculate the perimeter

• Determine the scale factor