Exploring Dilations in Geometry

The video tutorial explains the concept of dilation in geometry, focusing on mapping one line onto another by selecting a center and a scale factor. Initially, the origin is chosen as the center with a scale factor of 2, demonstrating how points on a line move further from the center. However, this approach only stretches the line onto itself. To achieve the desired mapping, a new center not on the line is selected, with a scale factor of 3, effectively mapping line a onto line b. The tutorial emphasizes the importance of choosing the right center and scale factor for successful dilation.

What is the first step in defining a dilation that maps line a onto line b?

• Finding the midpoint

• Calculating the distance

• Drawing the lines

• Choosing a center and a scale factor

If the center of dilation is at the origin and the scale factor is 2, what happens to a point (3,3) on line a?

• It moves to (9,9)

• It stays at (3,3)

• It moves to (1.5,1.5)

• It moves to (6,6)

How far does a point that is 3 units away from the origin move after a dilation with a scale factor of 2?

• 3 units

• 9 units

• 1.5 units

• 6 units

What happens to a line when the center of dilation is on the line?

• It maps onto itself

• It disappears

• It rotates

• It changes slope

Why does a line with infinite length map onto itself after dilation?

• Because it stretches and squeezes but remains infinite

• Because it changes direction

• Because it rotates

• Because it becomes finite

What is the chosen center of dilation to map line a onto line b in the example?

• (2,3)

• (0,0)

• (1,1)

• (3,2)

What is the scale factor used to map line a onto line b when the center is at (3,2)?

• 4

• 1

• 2

• 3

How far does a point 1 unit to the left of the center of dilation move with a scale factor of 3?

• 2 units to the left

• 4 units to the left

• 1 unit to the left

• 3 units to the left

Why was the center (3,2) chosen for the dilation?

• It was the origin

• It was the only option

• It fit nicely on the grid and was easy to calculate

• It was the midpoint of the lines

What is the final step after choosing the center and scale factor for dilation?

• Checking the answer

• Drawing the lines

• Calculating the distance

• Finding the midpoint