To solve the problem, we follow these steps:
1. Identify the given points and the fraction:
- Point [tex]\( A \)[/tex] is at [tex]\(-5\)[/tex].
- Point [tex]\( B \)[/tex] is at [tex]\(5\)[/tex].
- We are asked to find the coordinate of point [tex]\( C \)[/tex], which is [tex]\(\frac{1}{5}\)[/tex] of the way from [tex]\( A \)[/tex] to [tex]\( B \)[/tex].
2. Calculate the distance between points [tex]\( A \)[/tex] and [tex]\( B \)[/tex]:
- The distance between [tex]\( A \)[/tex] and [tex]\( B \)[/tex] can be found by subtracting the coordinate of [tex]\( A \)[/tex] from the coordinate of [tex]\( B \)[/tex]:
[tex]\[
\text{Distance}_{AB} = B - A = 5 - (-5) = 5 + 5 = 10
\][/tex]
3. Determine the fraction of this distance:
- Since point [tex]\( C \)[/tex] is [tex]\(\frac{1}{5}\)[/tex] of the way from [tex]\( A \)[/tex] to [tex]\( B \)[/tex], we need to calculate [tex]\(\frac{1}{5}\)[/tex] of the distance:
[tex]\[
\text{Fraction of Distance} = \frac{1}{5} \times 10 = 2
\][/tex]
4. Find the coordinate of point [tex]\( C \)[/tex]:
- Point [tex]\( C \)[/tex] is [tex]\(\frac{1}{5}\)[/tex] of the way from [tex]\( A \)[/tex] to [tex]\( B \)[/tex]. This means that [tex]\( C \)[/tex] is 2 units away from [tex]\( A \)[/tex] in the direction towards [tex]\( B \)[/tex].
- Since [tex]\( A \)[/tex] is at [tex]\(-5\)[/tex], moving 2 units towards [tex]\( B \)[/tex] (positive direction) will place [tex]\( C \)[/tex] at:
[tex]\[
C = A + \text{Fraction of Distance} = -5 + 2 = -3
\][/tex]
So, the coordinate of point [tex]\( C \)[/tex] is [tex]\(-3\)[/tex].
Thus, the coordinate of [tex]\( C \)[/tex] is [tex]\( \boxed{-3} \)[/tex].
