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
Circle 1 is congruent to circle 2.
Circle 1 and circle 2 have the same center.
Circle 2 is a dilation of circle 1 with a scale factor of 3.6.
Circle 1 is a dilation of circle 2 with a scale factor of 4.
Can someone answer this questions for me? I have answered all other questions correctly, but i'm stumped on this one.?
2017-02-17 2:13 am
回答 (1)
2017-02-17 2:19 am
All circles are similar. No matter how much you scale a circle it looks like every other circle. Only if the two circles have the same radius will they be congruent. Since the radii are different, the first statement isn't true.
The location of the centers doesn't matter for determining if two circles are similar (or congruent), but these two circles do have the same center. That doesn't tell you if they are similar or congruent, so we can ignore the second statement.
Now look at how the radii are related. In other words, take the ratio to determine the scale factor.
Circle 1 has a radius of 4.8
Circle 2 has a radius of 1.2
4.8 / 1.2 = 4
So circle 1 is scaled up by a factor of 4. Hence the third statement isn't correct but the fourth statement is.
Answer:
d. Circle 1 is a dilation of circle 2 with a scale factor of 4.
The location of the centers doesn't matter for determining if two circles are similar (or congruent), but these two circles do have the same center. That doesn't tell you if they are similar or congruent, so we can ignore the second statement.
Now look at how the radii are related. In other words, take the ratio to determine the scale factor.
Circle 1 has a radius of 4.8
Circle 2 has a radius of 1.2
4.8 / 1.2 = 4
So circle 1 is scaled up by a factor of 4. Hence the third statement isn't correct but the fourth statement is.
Answer:
d. Circle 1 is a dilation of circle 2 with a scale factor of 4.
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