To determine the location of the point that is [tex]\(\frac{2}{7}\)[/tex] of the way from [tex]\(A = 18\)[/tex] to [tex]\(B = 4\)[/tex], we can follow these steps:
1. Calculate the distance from [tex]\(A\)[/tex] to [tex]\(B\)[/tex]:
The distance from [tex]\(A\)[/tex] to [tex]\(B\)[/tex] can be found by subtracting [tex]\(A\)[/tex] from [tex]\(B\)[/tex]:
[tex]\[
\text{Distance} = B - A = 4 - 18 = -14
\][/tex]
The negative sign indicates that [tex]\(B\)[/tex] is to the left of [tex]\(A\)[/tex] on the number line.
2. Determine the fraction of the distance:
Since we are dealing with [tex]\(\frac{2}{7}\)[/tex] of the distance, multiply the distance by this fraction:
[tex]\[
\frac{2}{7} \times \text{Distance} = \frac{2}{7} \times -14 = -4
\][/tex]
This result shows that we are moving 4 units to the left from [tex]\(A\)[/tex].
3. Find the location on the number line:
To find the actual location, subtract this value from [tex]\(A\)[/tex]:
[tex]\[
\text{Point location} = A + \left(\frac{2}{7} \times \text{Distance}\right) = 18 + (-4) = 14
\][/tex]
So, the location of the point that is [tex]\(\frac{2}{7}\)[/tex] of the way from [tex]\(A = 18\)[/tex] to [tex]\(B = 4\)[/tex] is [tex]\(14\)[/tex].
Thus, the correct answer is:
A. 14
