Answer:
The scale factor is [tex]\frac{1}{2}[/tex].
Step-by-step explanation:
The given rule of dilation is
[tex]D_{O,K}=(10,0)\rightarrow (5, 0)[/tex]
It means the figure is dilated by scale factor K with center at origin.
If a figure dilated by scale factor K center at origin, then the scale factor is
[tex]K=\frac{\text{x-coordinate of image}}{\text{x-coordinate of preimage}}[/tex]
The x-coordinate of image is 5 and the x-coordinate of preimage is 10. So, the scale factor is
[tex]K=\frac{5}{10}[/tex]
[tex]K=\frac{1}{2}[/tex]
Therefore the scale factor is [tex]\frac{1}{2}[/tex].
