We know that <span>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.
</span>we have that <span>Circle 1 is centered at (4,3) and has a radius of 5 centimeters </span><span> Circle 2 is centered at (6,-2) and has a radius of 15 centimeters </span> step 1 <span>Move the center of the circle 1 onto the center of the circle 2 </span>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 <span>The circles are now concentric (they have the same center) </span> step 2 A dilation is needed to increase the size of circle 1<span> to coincide with circle 2 </span> 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<span> will map one circle onto the other, thus proving that the circles are similar</span>
