To determine the location of the point on the number line that is [tex]\(\frac{3}{5}\)[/tex] of the way from [tex]\(A = 2\)[/tex] to [tex]\(B = 17\)[/tex], we need to follow a series of steps.
1. Calculate the distance between [tex]\(A\)[/tex] and [tex]\(B\)[/tex]:
We first find the distance between the points [tex]\(A\)[/tex] and [tex]\(B\)[/tex] on the number line. This distance is the difference between the coordinates of [tex]\(B\)[/tex] and [tex]\(A\)[/tex].
[tex]\[
\text{Distance} = B - A = 17 - 2 = 15
\][/tex]
2. Determine the fraction of this distance:
We need to find [tex]\(\frac{3}{5}\)[/tex] of this distance. Therefore, we multiply the total distance by the fraction [tex]\(\frac{3}{5}\)[/tex]:
[tex]\[
\text{Fraction of Distance} = \frac{3}{5} \times 15 = 3 \times 3 = 9
\][/tex]
3. Find the location of the point:
Starting from point [tex]\(A\)[/tex], we move [tex]\(\frac{3}{5}\)[/tex] of the way toward point [tex]\(B\)[/tex]. Hence, we add the fraction of the distance to the coordinate of point [tex]\(A\)[/tex]:
[tex]\[
\text{Position} = A + \text{Fraction of Distance} = 2 + 9 = 11
\][/tex]
Therefore, the location of the point on the number line that is [tex]\(\frac{3}{5}\)[/tex] of the way from [tex]\(A = 2\)[/tex] to [tex]\(B = 17\)[/tex] is at 11.
The correct answer is [tex]\( \boxed{11} \)[/tex].
