Question

Circle 1 is centered at (−4, 5) and has a radius of 2 centimeters. Circle 2 is centered at (2, 1) and has a radius of 6 centimeters.
What transformations can be applied to Circle 1 to prove that the circles are similar?


Enter your answers in the boxes


The circles are similar because you can translate Circle 1 using the transformation rule (blank, blank) and then dilate it using a scale factor of blank.

Answer 1

If you translate circle 1 with the vector (6,-4), the center will become

$(-4,5)+(6,-4) = (-4+6,5-4)=(2,1)$

So, circles 1 and 2 are now concentric. The radii are, respectively, 2 and 6. This means that, if we dilate circle 1 with a scale factor of 3, its radius will become 6 as well.

After this two transformations, both circles will have center (2,1) and radius 6.