Exploring Dilating Lines in Geometry

This video tutorial covers the concept of dilating lines by combining skills from previous lessons on dilations and writing line equations. It provides step-by-step examples of how to dilate lines using different scale factors and centers, including a case where the center is not at the origin. The tutorial emphasizes the importance of maintaining parallelism in dilated lines and guides viewers through the process of writing new line equations after dilation.

What two skills are being combined in this lesson?

• Writing equations and solving inequalities

• Graphing and solving equations

• Dilation and writing equations of lines

• Dilation and graphing

What is the first step in dilating a line?

• Pick a point on the line

• Find the center of dilation

• Draw the original line

• Calculate the scale factor

In the first example, what is the new y-intercept after dilation?

• 8

• 2

• 4

• 6

Why do dilated lines remain parallel to the original line?

• Because the y-intercept changes

• Because the x-intercept changes

• Because dilations make lines parallel

• Because the slope changes

What is the scale factor used in the second example?

• 2

• 4

• 1

• 3

In the second example, what is the new y-intercept after dilation?

• -8

• -4

• -2

• -6

In the third example, what is the center of dilation?

• (0, 0)

• (1, 1)

• (2, 2)

• (3, 2)

What is the new point that the line goes through after dilation in the third example?

• (2, 4)

• (-1, 4)

• (1, 4)

• (0, 4)

What should you do after solving the final problem?

• Check your answer

• Ask for help

• Skip it

• Redo the problem

What is the final step in writing the equation of a dilated line?

• Find the slope

• Plug into y = mx + b

• Graph the line

• Find the y-intercept