To determine the point that is [tex]\(\frac{1}{5}\)[/tex] of the way from 0 to -19 on the number line, we can follow these steps:
1. Identify the starting and ending points. Here, the starting point is 0 and the ending point is -19.
2. Calculate the total distance between these two points. This is simply [tex]\(-19 - 0 = -19\)[/tex].
3. Since we want to find the point that is [tex]\(\frac{1}{5}\)[/tex] of the way from 0 to -19, we need to scale the total distance by [tex]\(\frac{1}{5}\)[/tex].
[tex]\[
\text{Fractional Distance} = \frac{1}{5} \times -19 = -3.8
\][/tex]
4. Starting from the original point 0, move this fractional distance in the direction towards -19.
[tex]\[
\text{Position} = 0 + (-3.8) = -3.8
\][/tex]
Thus, the point that is [tex]\(\frac{1}{5}\)[/tex] of the way from 0 to -19 on the number line is [tex]\(-3.8\)[/tex].
Therefore, the correct answer is [tex]\( -3.8 \)[/tex].
