To find the point on the number line that is [tex]\(\frac{1}{5}\)[/tex] of the way from the point 0 to the point [tex]\(-19\)[/tex], we will follow a structured approach:
1. Identify the positions of the given points:
- The first point ([tex]\( \text{point1} \)[/tex]) is located at 0.
- The second point ([tex]\( \text{point2} \)[/tex]) is located at [tex]\(-19\)[/tex].
2. Calculate the distance between the two points:
- The distance can be calculated by subtracting the coordinates of point1 from point2:
[tex]\[
\text{Distance} = -19 - 0 = -19
\][/tex]
3. Determine the fractional distance:
- We need to find the point that is [tex]\(\frac{1}{5}\)[/tex] of the way from 0 to [tex]\(-19\)[/tex].
- Therefore, we multiply the total distance by [tex]\(\frac{1}{5}\)[/tex]:
[tex]\[
\text{Fractional Distance} = \frac{1}{5} \times (-19) = -\frac{19}{5} = -3.8
\][/tex]
4. Locate the target point:
- Starting from point1 (which is 0), if we move [tex]\(-3.8\)[/tex] units (the fractional distance) towards point2, we reach the target point. Therefore:
[tex]\[
\text{Target Point} = 0 + (-3.8) = -3.8
\][/tex]
Putting it all together, the point on the number line that is [tex]\(\frac{1}{5}\)[/tex] of the way from 0 to [tex]\(-19\)[/tex] is [tex]\(-3.8\)[/tex].
The distance between the two points is [tex]\(-19\)[/tex] units, and the target point on the number line is [tex]\(-3.8\)[/tex].
