Question

Circle A, centered at A(-4, 3) with radius of 3 cm is translated so that it is concentric with Circle B, centered at B(8. 5) with a radius of 9cm. Which transformation would now establish that the two circles are similar?

Answer 1

Hello!

The answer is: Dilation with center B and scale factor on A.

Why?

Two circles will be always similar because of the ratio proportionality.

Since all circles are similar, we need to prove it by using the following formula:

$C_{A} =C_{B}\\C_{A}= 2*\pi *r_{A} =2*\pi *r_{B}\\\frac{r_{B} }{r_{A} } =\frac{9}{3} =3$

The number that multiplies Circle A radius to make it similar to Circle B radius is 3.

$r_{A}*3=r_{B}=9cm$

Have a nice day!