Circle Dilation and Angle Measures

The video tutorial explains the concept of dilating a circle with a scale factor of three, centered at the origin. It covers how to calculate new positions of points after dilation and proves the similarity of two circles by comparing their diameters and circumferences. The tutorial also discusses the importance of angle congruence and proportionality in determining circle similarity. It concludes by affirming that all circles are similar due to these properties.

What is the center of dilation in the given problem?

• Point C

• The origin

• Point A

• Point B

What is the scale factor used to dilate the circle?

• 4

• 3

• 5

• 2

How do you determine the new radius after dilation?

• Subtract the scale factor from the original radius

• Multiply the original radius by the scale factor

• Add the scale factor to the original radius

• Divide the original radius by the scale factor

What is the new position of point B after dilation?

• (4, 8)

• (2, 4)

• (6, 12)

• (8, 16)

What is the goal of proving the two circles are similar?

• To show they have proportional sides and congruent angles

• To show they have the same diameter

• To show they have the same circumference

• To show they have the same area

What is the diameter of the preimage circle?

• 4 units

• 2 units

• 6 units

• 8 units

What is the diameter of the image circle after dilation?

• 12 units

• 6 units

• 8 units

• 10 units

What is the simplified ratio of the diameters of the image to the preimage?

• 1:2

• 2:3

• 3:1

• 1:3

How do you calculate the circumference of a circle?

• 2πr

• πr²

• πd

• 2πd

What is the circumference of the preimage circle?

• 4π

• 2π

• 6π

• 8π