Dilation of Lines and Their Properties

The video tutorial covers the concept of dilations in geometry, focusing on lines. It explains two key scenarios: when the center of dilation is on the line, resulting in the same line, and when the center is not on the line, resulting in parallel lines. The tutorial includes examples with different lines and centers, demonstrating how to calculate new line equations after dilation. It concludes with multiple-choice questions to reinforce the concepts.

What happens to a line when it is dilated with the center on the original line?

• The line remains the same.

• The line disappears.

• The line becomes shorter.

• The line becomes a curve.

If the center of dilation is not on the original line, what is the relationship between the original and the dilated line?

• They intersect at one point.

• They overlap completely.

• They are perpendicular.

• They are parallel.

In the example where the center is at the origin and the scale factor is 3/2, what is the new y-intercept if the original line is y = 2x - 4?

• -2

• -8

• -6

• -4

When the center of dilation is on the line, what happens to the dilated line?

• It disappears.

• It becomes a different line.

• It remains the same as the original line.

• It becomes a curve.

In the example where the center is not on the line and the scale factor is 2, what is the slope of the new line if the original line is y = 2x + 1?

• 0

• 3

• 2

• 1

What is the result of dilating a line with a center not on the line and a scale factor of 1/2?

• The new line is twice as far from the center.

• The new line is half as far from the center.

• The new line is the same as the original.

• The new line is perpendicular to the original.