To compare the length from point B to point C (denoted as BC) with the length from point B to point D (denoted as BD), we use the fraction [tex]\(\frac{BC}{BD}\)[/tex].
Given:
- BC is the length from B to C, which is 2 units.
- BD is the length from B to D, which is 3 units.
The fraction that compares these two lengths is:
[tex]\[
\frac{\text{BC}}{\text{BD}} = \frac{2}{3}
\][/tex]
To verify, we can check this fraction:
[tex]\[
\frac{BC}{BD} = \frac{2}{3} \approx 0.6667
\][/tex]
Comparing this to the given options:
- [tex]\(\frac{2}{3} \approx 0.6667\)[/tex]
- [tex]\(\frac{5}{2} = 2.5\)[/tex]
- [tex]\(\frac{2}{5} = 0.4\)[/tex]
- [tex]\(\frac{3}{2} = 1.5\)[/tex]
Clearly, the fraction that compares BC to BD is [tex]\(\frac{2}{3}\)[/tex].
Therefore, the correct answer is:
[tex]\[
\boxed{\frac{2}{3}}
\][/tex]
