Question

Circle 1 has center (−6, 2) and a radius of 8 cm. Circle 2 has center (−1, −4) and a radius 6 cm.

What transformations can be applied to Circle 1 to prove that the circles are similar?

Enter your answers in the boxes. Enter the scale factor as a fraction in 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

Answer 1

@Shadow

Answer 2

@tigerlover

Answer 3

@umm

Answer 4

@563blackghost

Answer 5

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. ----> 4/3

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 ​4/3.