# Circle 1 is centered at 4,3 and has a radius of 5 centimeters circle 2 is centered at 6,-2 and has a radius of 15 centimeters. What transformatons can be applied to circle one to prove that the aircles are similar?

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calculistaWe know that Figures can be proven similar if one, or more, similarity transformations (reflections, translations, rotations, dilations) can be found that map one figure onto another. In this problemÂ to prove circle 1 and circle 2Â are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another. we have that Â Circle 1 is centered at (4,3) and has a radius of 5 centimeters Â Circle 2 is centered at (6,-2) and has a radius of 15 centimeters step 1 Move the center of the circle 1Â onto the center of the circle 2 the transformation has the following rule (x,y)--------> (x+2,y-5) so (4,3)------> (4+2,3-5)-----> (6,-2) so center circle 1 is now equal to center circle 2Â The circles are now concentric (they have the same center) step 2 A dilation is needed to increase the size of circle 1Â to coincide with circleÂ 2 scale factor=radius circle 2/radius circle 1-----> 15/5----> 3 radius circle 1 will be=5*scale factor-----> 5*3-----> 15 cm radius circle 1 is nowÂ equal toÂ radiusÂ circle 2Â A translation, followed by a dilationÂ will map one circle onto the other, thus proving that the circles are similar