Prove that the two circles shown below are similar.

Circle X is shown with a center at negative 2, 8 and a radius of 6. Circle Y is shown with a center of 4, 2 and a radius of 3.


The picture in the attached figure we have that circle x center point is (-2,8) radius r=6 units the equation of a circle x is  (x+2)²+(y-8)²=6² circle y center point is (4,2) radius r=3 units the equation of a circle y is  (x-4)²+(y-2)²=3² we know that If I can transform circle x to circle y using only translations, rotations and scaling  (In the case of circles, no rotations are necessary)thencircle x and circle y are similar hence step 1 scaling radius circle x by a factor of 0.5 r=6 units----------> r=6*0.5--------> r=3 units step2 translate the center circle x (-2,8) 6 units at right 6 units down (x,y)--------> (x+6,y-6)(-2,8)-------->(-2+6,8-6)--------> (-4,2) now the circle x and the circle y have the same radius an the same center using only translation and scaling therefore circle x an circle y are similar

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