To find the [tex]\( X \)[/tex] coordinate of the point located [tex]\(\frac{1}{3}\)[/tex] of the distance from point [tex]\( X(1, 2) \)[/tex] to point [tex]\( Y(6, 7) \)[/tex], we can follow these steps:
1. Determine the horizontal distance between [tex]\( X \)[/tex] and [tex]\( Y \)[/tex]:
- The [tex]\( X \)[/tex]-coordinate of [tex]\( X \)[/tex] is [tex]\( 1 \)[/tex].
- The [tex]\( X \)[/tex]-coordinate of [tex]\( Y \)[/tex] is [tex]\( 6 \)[/tex].
The horizontal distance [tex]\( \Delta X \)[/tex] is:
[tex]\[
\Delta X = Y_x - X_x = 6 - 1 = 5
\][/tex]
2. Calculate the distance from [tex]\( X \)[/tex] to the desired point:
- We need the point that is located [tex]\(\frac{1}{3}\)[/tex] of this distance from [tex]\( X \)[/tex].
This means we need [tex]\(\frac{1}{3}\)[/tex] of [tex]\( 5 \)[/tex]:
[tex]\[
\text{Distance} = \frac{1}{3} \times 5 = \frac{5}{3} \approx 1.6666666666666667
\][/tex]
3. Find the [tex]\( X \)[/tex] coordinate of the desired point:
Starting from point [tex]\( X \)[/tex], we move this calculated distance towards point [tex]\( Y \)[/tex]:
[tex]\[
X_{\text{coordinate}} = X_x + \frac{5}{3} = 1 + 1.6666666666666667 \approx 2.6666666666666665
\][/tex]
Therefore, the [tex]\( X \)[/tex] coordinate of the point located [tex]\(\frac{1}{3}\)[/tex] the distance from [tex]\( X \)[/tex] to [tex]\( Y \)[/tex] is approximately:
[tex]\[
2.6666666666666665
\][/tex]
Given the answer choices, the closest option is:
[tex]\[
2.7
\][/tex]
So, the correct choice is:
2.7
