Answer: The required scale factor is 1.5.
Step-by-step explanation: Given that the figure 1 is dilated to figure 2.
We are to find the scale factor of dilation.
We know that
the scale factor of dilation is defined as
[tex]S=\dfrac{\textup{length of a side of the dilated figure}}{\textup{length of the corresponding side of the original figure}}.[/tex]
From the picture, we note that
length of a side of the original figure 1, l = 6 units
and
length of the corresponding side of the dilated figure 2, l' = 9 units.
Therefore, the required scale factor of dilation is given by
[tex]S=\dfrac{l'}{l}=\dfrac{9}{6}=\dfrac{3}{2}=1.5.[/tex]
Thus, the required scale factor is 1.5.
