Question

two circles share the same center but have radii of 7 and 28. what is the required transformation?
a. reflection
b. dilation
c. translation
d. rotation

what transformation is used to uniformly scale all points of a circle outward or inward while preserving its shape?
a. reflection
b. rotation
c. dilation
d. translation

circle ( c_1 ) has a radius of 6 and is centered at ( (4, -1) ). circle ( c_2 ) has a radius of 12 and shares the same center. what is needed to map circle ( c_1 ) onto circle ( c_2 )?
a. reflection
b. rotation
c. dilation
d. translation

if there are two different radii of the same circle, what can be said about their size?
a. they are equal to the scale factor multiplied by the radius.
b. they are equal in length.
c. they are perpendicular to each other.
d. they are individually equal to the diameter of the circle.

Explanation:

• First question:
• Reflection flips a figure over a line.
• Translation slides a figure.
• Rotation turns a figure around a point.
• Dilation changes the size of a figure. Since the circles have the same center but different radii (size change), dilation is the transformation.
• Second question:
• Reflection flips, rotation turns, translation slides.
• Dilation scales a figure (changes size while preserving shape). So dilation is the transformation.
• Third question:
• Reflection, rotation, and translation don't change the size of a figure.
• Dilation changes the size. Since \(C_1\) (radius \(6\)) and \(C_2\) (radius \(12\)) have the same center but different radii (size change), dilation is needed.
• Fourth question:
• By the definition of a circle, all radii of a single circle are equal in length.

Answer:

1. b. Dilation
2. c. Dilation
3. c. Dilation
4. b. They are equal in length.