Circle 1: center (8, 5) and radius 6Circle 2: center (−2, 1) and radius 2What transformations can be applied to Circle 1 to prove that the circles are similar? What scale factor does the dilation from Circle 1 to Circle 2 have?Show your work

Answer:Part 1) A translation, followed by a dilation will map one circle onto the other, thus proving that the circles are similarPart 2) The scale factor is equal to 1/3Step-by-step explanation:we know thatFigures 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 (8,5) and has a radius of 6 units Circle 2 is centered at (-2,1) and has a radius of 2 unitsstep 1Move the center of the circle 1 onto the center of the circle 2the transformation has the following rule(x,y)--------> (x-10,y-4)That means----> The translation is 10 units to the left and 4 units downso(8,5)------> (8-10,5-4)-----> (-2,1)center circle 1 is now equal to center circle 2  The circles are now concentric (they have the same center)step 2A dilation is needed to decrease the size of circle 1 to coincide with circle 2The scale factor is equal to divide the radius of circle 2 by the radius of circle 1scale factor=radius circle 2/radius circle 1-----> 2/6=1/3radius circle 1 will be=6*scale factor-----> 6*(1/3)=2 unitsradius circle 1 is now equal to radius circle 2  thereforeA translation, followed by a dilation will map one circle onto the other, thus proving that the circles are similar