# 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?

## Answers

If you are not satisfied with the answer or you can’t find one, then try to use the search above or find similar answers below.

Find similar answersMathematics, added 2020-11-29 19:01:16

Mathematics, added 2020-11-29 17:58:05

Mathematics, added 2020-11-28 12:01:08

Mathematics, added 2020-11-28 10:39:39

Mathematics, added 2020-11-28 02:39:33

Mathematics, added 2020-11-28 00:50:16

Mathematics, added 2020-11-27 06:39:25

A circle has the equation x2 + y2 – x + 10y + 13 = 0. What is the radius of this circle? ...

Mathematics, added 2020-11-27 05:26:05

A circle has the equation x2 + y2 – x + 10y + 13 = 0. What is the radius of this circle? ...

Answered by

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 problem to prove circle 1 and circle 2 are similar, a translation and a scale factor (from a dilation) will be found to map one circle onto another. we have that 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 step 1 Move the center of the circle 1 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 2 The circles are now concentric (they have the same center) step 2 A dilation is needed to increase the size of circle 1 to coincide with circle 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 now equal to radius circle 2 A translation, followed by a dilation will map one circle onto the other, thus proving that the circles are similar