Question

the blue figure is a dilation of the red figure. identify the type of dilation and find the scale factor.
the dilation is an enlargement
the scale factor is

Explanation:

Step1: Pick corresponding vertices

Take vertex $A(1,3)$ (red) and $A'(2,6)$ (blue); $C(1,1)$ (red) and $C'(2,2)$ (blue).

Step2: Calculate scale factor

Scale factor $k = \frac{\text{Blue vertex coordinate}}{\text{Red vertex coordinate}}$.
For x-coordinates: $k=\frac{2}{1}=2$; for y-coordinates: $k=\frac{6}{3}=2$ or $k=\frac{2}{1}=2$.

Answer:

The dilation is an enlargement
The scale factor is $2$