To determine the exact lengths of segments $AC$ and $BC$, we will use the property of similar triangles that states corresponding sides are proportional. The proportions can be set up as:

$\frac{AB}{DE} = \frac{BC}{EF} = \frac{AC}{DF}$

From the diagram:

• $AB = 4.8$, $DE = 1$
• $BC = 3$, $EF = x$ (to be calculated)
• $AC = 6$, $DF = y$ (to be calculated)

1. Using the first ratio $\frac{AB}{DE}$, calculate the scale factor: $\text{Scale factor} = \frac{AB}{DE} = \frac{4.8}{1} = 4.8$

2. Use this scale factor to find the lengths of $EF$ and $DF$:

   • $EF = \frac{BC}{\text{Scale factor}} = \frac{3}{4.8} = 0.625$
   • $DF = \frac{AC}{\text{Scale factor}} = \frac{6}{4.8} = 1.25$

Thus, the exact lengths are:

• $EF = 0.625$
• $DF = 1.25$