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Circle 1 has a center (-4,5) and a radius of 12 cm. Circle 2 has center (2,-3) and radius 18 cm.

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

The circles are similar because of the transformation rule (Blank 1, Blank 2) is it plus or minus the number) can be applied to circle 1 and then dilate it using a scale factor of Blank 3.

Example of what to put in blank 1 = x+1 OR x-2

Example of what to put in blank 2 = y+3 OR y-2

Example of what to put in blank 3 = 1/2 OR 7/4



Answer :

To prove that the circles are similar, we need to find a transformation that can be applied to Circle 1 to make it congruent to Circle 2, followed by a dilation using a scale factor.

Given:
- Circle 1: Center (-4, 5), Radius 12 cm
- Circle 2: Center (2, -3), Radius 18 cm

Transformation Rule:
To move Circle 1's center to coincide with Circle 2's center, we need to add the difference in x and y coordinates:
- Blank 1: x + 6 (to move from -4 to 2)
- Blank 2: y - 8 (to move from 5 to -3)

Scale Factor:
Since the circles are similar, the ratio of their radii will be the scale factor:
- Scale Factor = Radius of Circle 2 / Radius of Circle 1
- Scale Factor = 18 cm / 12 cm = 3/2

Putting it all together:
The transformation rule that can be applied to Circle 1 is (x + 6, y - 8), and then dilating it using a scale factor of 3/2.

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