Question

question 4 points 3
circle a: center (7, 0) and radius 5
circle b: center (10, 0) and radius 2
which of the following transformation is performed from circle b to circle a to prove that the two circles are similar?

translation: 3 units left and scale factor: \\(\frac{2}{5}\\)

translation: 3 units right and scale factor: \\(\frac{2}{5}\\)

translation: 3 units left and scale factor: \\(\frac{5}{2}\\)

translation: 3 units right and scale factor: \\(\frac{5}{2}\\)

complete later complete

Explanation:

Step1: Analyze Translation

To move from the center of Circle B \((10, 0)\) to the center of Circle A \((7, 0)\), we calculate the horizontal shift. Since \(10 - 3 = 7\), we need to translate 3 units to the left.

Step2: Analyze Scale Factor

The radius of Circle B is \(r_B = 2\) and the radius of Circle A is \(r_A = 5\). The scale factor from Circle B to Circle A is \(\frac{r_A}{r_B}=\frac{5}{2}\).

Answer:

Translation: 3 units left and scale factor: \(\frac{5}{2}\) (corresponding to the third option: "Translation: 3 units left and scale factor: \(\frac{5}{2}\)")