Circle 1 has a center (−4, 5) and a radius of 6 cm. Circle 2 has (2, −3) and a radius of 9 cm. What transformations can be applied to Circle 1 to prove that the circles are similar? Enter your answers in the blanks. Enter the scale factor as a fraction in the simplest form. The circles are similar because the transformation rule (___ , ___ ) can be applied to Circle 1 and then dilate it using a scale factor of ___/___

The circles are similar because the transformation rule (+ 5 , - 6) can be applied to Circle 1 and then dilate it using a scale factor of ​3/4.

Step-by-step explanation:

All the circles are similar.

That is because you can transform one circle onto another by two similarity operations: translation and dilation (scale factor).

For these two circles you have to translate the center of circle 1 to the center of circle 2, which will make that the two circles are concentric (have the same center).

The two centers are (-6,2) and (-1,- 4). To move the center (-6, 2) to (-1,4) you have to shift it 5 units to the right and 6 units down:

- 6 + 5  = - 1

2 - 6 = - 4.

After this translation, you dilate the circle with smaller radius using a scale factor equal to the ratio of the bigger radius to the smaller radius: 8/6 = 4/3.

Enter the scale factor as a fraction in simplest form. 3/4

The circles are similar because the transformation rule (+5 , - 6) can be applied to Circle 1 and then dilate it using a scale factor of ​3/4.

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