Question

Circle 1 is centered at (5, 8) and has a radius of 8 centimeters. Circle 2 is centered at (1, −2) and has a radius of 4 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 (
,
) and then dilate it using a scale factor of
_____

Answer 1

In order to carry out this transformation, using similarity transformation the following steps must be applied

1) From the center of the second circle to the center of the first circle, a vector has to be drawn

2) The second circle must be carried to the first circle by this vector.

3) Finally, the transformation is done by this dilation. Indeed, everything comes to the theorem for the similarity of the circles that all circles are similar.

And the scale factor is $\frac{r_{1} }{r_{2} }= \frac{8}{4}=2$