The scale factor is the ratio between equivalent sides and is the same for any pairs of sides, so:
For exercise 1:
[tex]\begin{gathered} scalefactor=\frac{A^{\prime}B^{\prime}}{AB}=\frac{A^{\prime}C^{\prime}}{AC}=\frac{2}{4}=\frac{1}{2}=0.5 \\ \frac{x}{9}=\frac{2}{4} \\ x=\frac{2}{4}\cdot9 \\ x=\frac{9}{2}=4.5 \\ \end{gathered}[/tex]
The scale factor is 1/2 = 0.5 and x = 9/2 = 4.5.
For exercise 2:
[tex]\begin{gathered} \text{scale factor=}\frac{E^{\prime}F^{\prime}}{EF}=\frac{F^{\prime}D^{\prime}}{FD}=\frac{7.5}{5}=1.5 \\ \frac{x}{8}=1.5 \\ x=1.5\cdot8 \\ x=12 \end{gathered}[/tex]
The scale factor is 1.5 and x = 12
