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1. Why is circle 1 similar to circle 2?

Circle 1: center (−1, 10) and radius 4.8
Circle 2: center (−1, 10) and radius 1.2

A) Circle 1 is a dilation of circle 2 with a scale factor of 4.
B) Circle 1 and circle 2 have the same center.
C) Circle 2 is a dilation of circle 1 with a scale factor of 3.6.
D) Circle 1 is congruent to circle 2.

2. Which transformations can be used to show that circle M is similar to circle N?

Circle M: center (−1, 10) and radius 3
Circle N: center (0, 10) and radius 15

A) Circle N is a translation of circle M, 1 unit right.
B) Circle M is a dilation of circle N with a scale factor of 12.
C) Circle N is a dilation of circle M with a scale factor of 5.
D) Circle M and circle N are congruent.

(You can choose more than one option.)

3. According to these three facts, which statements are true?

- Circle M has center (1, 10) and radius 12.
- Circle N is a translation of circle M, 1 unit left.
- Circle N is a dilation of circle M with a scale factor of 3.

A) The radius of circle N is 12.
B) The center of circle N is (0, 10).
C) Circle N and circle M have equal diameters.
D) Circle M and circle N are similar.

(Again, you can choose more than one option.)

4. Suppose x is any positive number.

Circle 1: center (5, 4) and radius 5x
Circle 2: center (5, 4) and radius 2x

Why is circle 1 similar to circle 2?

A) Circle 1 is a dilation of circle 2 with a scale factor of 2.5.
B) Circle 1 is congruent to circle 2.
C) Circle 1 and circle 2 have the same radius.
D) Circle 1 is a dilation of circle 2 with a scale factor of 0.4.

If someone could please help me with these questions, it would be very, very appreciated! Thank you to anyone who helps me.

### 1 Answer by Expert Tutors

Matt H. | PATIENT :-) Elem/Middle MATH and WRITING; HS SAT and COLLEGE ESSAYS!PATIENT :-) Elem/Middle MATH and WRITING...
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Shortcut for questions 1 and 2:

All circles are similar. They are all dilations of one another. That's why formulas for area and circumference always come down to the same magic number: pi.