Question

Circle A has center of (5, -2) and a radius of 7, and circle B has a center of (7, -8) and a radius of 35. What steps will help show that circle A is similar to circle B?
A.) Rotate circle A 90 degrees counterclockwise about the center.
B) Translate circle A using the rule (x-2, y+6).
C) Reflect circle A over the y-axis.
D) Dilate circle A by a scale factor of 5.

Answer 1

Answer:

Dilate circle A by a scale factor of 5.

Step-by-step explanation:

The only necessary condition for two circles to be similar, is for them to be able to have the same radius. The similarity of circles is independent from where the center of the circle is, so translations will not serve the purpose. By dilating the radius of circle A a factor of 5, will take it to have radius (7*5)=35 , getting to measure and have a representation like circle B.

Answer 2

Answer:

D) Dilate circle A by a scale factor of 5.

Step-by-step explanation:

The most reasonable transformation we could do to show the similarity between both circle is to dilate circle A by a scale factor of 5, that is, increases the sized of circle A five time, that will give a congruent circle to circle B. Because, as you can see, the radius of A is 7 and the radius of B is 35, their ratio is 5.

Remember that a similarity between circles is based on the radius, if they have the same radius, they are congruent, if they have proportional radius, they are similar.

So, in this case, they are proportional, which a ratio of 5, that's why dilating circle A 5 times is the best way to show the similarity.