Question

given: circle x with radius r and circle y with radius s
prove: circle x is similar to circle y.
translate x to y circle x ~ circle y dilate circle x by s/r
circle with center x has radius r circle with center y has radius s

Explanation:

Step1: State the given information

circle with center \( X \) has radius \( r \); circle with center \( Y \) has radius \( s \)

Step2: Translate circle \( X \) to \( Y \)

Translation is a rigid transformation that moves a figure without changing its shape or size.

Step3: Dilate circle \( X \) by \( \frac{s}{r} \)

Dilation is a transformation that changes the size of a figure. If we dilate a circle with radius \( r \) by a scale factor \( k=\frac{s}{r} \), the new radius is \( r\times\frac{s}{r}=s \)

Answer:

Statements	Reasons
translate \( X \) to \( Y \)	Translation (rigid transformation)
dilate circle \( X \) by \( \frac{s}{r} \)	Dilation (scale - factor transformation)
circle \( X\sim\) circle \( Y \)	Similarity (combination of translation and dilation)