Circle \( J \) is located in the first quadrant with center \( (a, b) \) and radius \( s \). Felipe transforms Circle \( J \) to prove that it is similar to any circle centered at the origin with radius \( t \). Which sequence of transformations did Felipe use? (A) Translate Circle \( J \) by \( (x+a, y+b) \) and dilate by a factor of \( \frac{t}{S} \). Translate Circle \( J \) by \( (x+a, y+b) \) and dilate by a factor of \( \frac{S}{t} \). (C) Translate Circle \( J \) by \( (x-a, y-b) \) and dilate by a factor of \( \frac{t}{s} \). (D) Translate Circle \( J \) by \( (x-a, y-b) \) and dilate by a factor of \( \frac{S}{t} \).

To determine the correct sequence of transformations that Felipe used to show that Circle \( J \) is similar to any circle centered at the origin with radius \( t \), we need to analyze the transformations involved. 1. **Translation**: Circle \( J \) is centered at \( (a, b) \). To move this circle to be centered at the origin \( (0, 0) \), we need to translate it by \( (-a, -b) \). This means we will adjust the coordinates of the circle's center from \( (a, b) \) to \( (0, 0) \). 2. **Dilation**: After translating the circle to the origin, we need to adjust its radius from \( s \) to \( t \). This is done through dilation. The factor for dilation will be \( \frac{t}{s} \) because we want to scale the radius \( s \) to become \( t \). Now, let's match this reasoning with the options provided: - **Option (A)**: Translate Circle \( J \) by \( (x+a, y+b) \) and dilate by a factor of \( \frac{t}{s} \). (Incorrect translation) - **Option (B)**: Translate Circle \( J \) by \( (x+a, y+b) \) and dilate by a factor of \( \frac{s}{t} \). (Incorrect translation and dilation) - **Option (C)**: Translate Circle \( J \) by \( (x-a, y-b) \) and dilate by a factor of \( \frac{t}{s} \). (Correct translation and dilation) - **Option (D)**: Translate Circle \( J \) by \( (x-a, y-b) \) and dilate by a factor of \( \frac{s}{t} \). (Correct translation but incorrect dilation) The correct sequence of transformations that Felipe used is: **(C) Translate Circle \( J \) by \( (x-a, y-b) \) and dilate by a factor of \( \frac{t}{s} \).**