Question

Which statement proves that the two circles are similar?The circles A and C are similar because A can be mapped onto C by a translation of 3 units to the right and 5units up, followed by a dilation about its center by a scale factor of 0.4.O The circles A and C are similar because A can be mapped onto C by a translation of 3 units to the right andunits up, followed by a dilation about its center by a scale factor of 2.5.The circles A and C are similar because A can be mapped onto C by a translation of 3 units to the left and 5units down, followed by a dilation about its center by a scale factor of 0.4.The circles A and C are similar because A can be mapped onto C by a translation of 3 units to the left and 5units down, followed by a dilation about its center by a scale factor of 2.5.

Answer 1

Step 1

Given;

Required;

Step 2

Find the radius;

$\begin{gathered} Radius\text{ of A =5} \\ Radius\text{ of B=2} \end{gathered}$

Step 3

Pick two coordinate points

$\begin{gathered} A=(3,4) \\ B=(0,-1) \end{gathered}$

Apply the right translation.

$\begin{gathered} From\text{ A to B} \\ 3\text{ units to the left \lparen3-3,4\rparen=\lparen0,4\rparen} \\ 5\text{ units down; \lparen0,4-5\rparen=\lparen0,-1\rparen} \end{gathered}$$\begin{gathered} Dilation\text{ by a scale factor of 2.5} \\ \frac{Radius\text{ of A}}{Radius\text{ of B}}=\frac{5}{2}=2.5 \end{gathered}$

Thus the answer is ;