Scale factor
Initial explanation
In order to find the scale factor of the dilation of ΔABC, we just need to divide any pair of the corresponding sides of both triangles. We have that the division of the corresponding sides will be always the same:
[tex]\frac{A^{\prime}C^{\prime}}{AC}=\frac{B^{\prime}C^{\prime}}{BC}=\frac{A^{\prime}B^{\prime}}{AB}=\text{scale factor}[/tex]
We are going to choose the first division:
[tex]\frac{A^{\prime}C^{\prime}}{AC}=\text{scale factor}[/tex]
Finding the scale factor
We have that AC = 5 and A'C' = 10:
Then:
[tex]\begin{gathered} \frac{A^{\prime}C^{\prime}}{AC}=\text{scale factor} \\ \downarrow \\ \frac{10}{5}=2 \end{gathered}[/tex]
The scale factor is 2.
And since the point C and C' are the same, the center is C.
Answer- A. center C and scale factor 2
