What point on the number line is [tex]$\frac{1}{5}$[/tex] of the way from the point 0 to the point -19?

A. [tex]-3.6[/tex]
B. [tex]-3.8[/tex]
C. [tex]-4[/tex]
D. [tex]-9.5[/tex]



Answer :

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].