Question

a circle is dilated with a scale factor of 2 and moved so its center aligns with another circles center. what transformations were applied?
a. dilation and translation
b. rotation and dilation
c. dilation and reflection
d. translation and reflection

what role does translation play in proving that all circles are similar?
a. scales the radius of one circle to match another
b. reflects one circle onto another
c. aligns the centers of two circles after dilation
d. rotates one circle to overlap another

the diameters of two circles are 12 and 30. what scale factor (k) is needed to map the smaller circle onto the larger circle?
a. 2
b. 3
c. 1.5
d. 2.5

a circle with radius ( r_1 = 5 ) is dilated to a circle with radius ( r_2 = 50 ). what is the scale factor (k)?
a. 1
b. 15
c. 5
d. 10

a circle with a radius of 3 is dilated to have a radius of 15. what is the scale factor (k) for the dilation?
a. 15
b. 3
c. 5
d. 10

which statement best explains why all circles are similar?
a. only circles that share the same center are similar.
b. all circles can be mapped onto one another using dilations and translations.
c. all circles have equal circumference.
d. only circles with the same radius are similar.

two circles share the same center but have radii of 7 and 28. what is the required transformation?

Explanation:

Step1: Analyze the first question

Dilation changes the size (scale factor of 2), and moving (aligning centers) is translation.

Step2: Analyze the second question

Translation moves the circle (aligns centers after dilation which scales).

Step3: Analyze the third question

Scale factor \(k=\frac{\text{larger diameter}}{\text{smaller diameter}}=\frac{30}{12} = 2.5\)

Step4: Analyze the fourth question

Scale factor \(k=\frac{r_2}{r_1}=\frac{50}{5}=10\)

Step5: Analyze the fifth question

Scale factor \(k=\frac{15}{3}=5\)

Step6: Analyze the sixth question

All circles can be mapped using dilation (scale) and translation (move), so they are similar.

Step7: Analyze the seventh question (assuming it's about transformation for same - center circles with different radii)

Dilation (since centers are same, just size change)

Answer:

1. a. Dilation and translation
2. c. Aligns the centers of two circles after dilation
3. d. 2.5
4. d. 10
5. c. 5
6. b. All circles can be mapped onto one another using dilations and translations.
7. Dilation