To find 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 can follow these steps:
1. Determine the distance between [tex]\(A\)[/tex] and [tex]\(B\)[/tex]:
[tex]\[
\text{Distance between } A \text{ and } B = B - A
\][/tex]
Substituting the given values:
[tex]\[
\text{Distance between } A \text{ and } B = 17 - 2 = 15
\][/tex]
2. Calculate [tex]\(\frac{3}{5}\)[/tex] of this distance:
[tex]\[
\text{Fraction of distance} = \frac{3}{5} \times \text{Distance between } A \text{ and } B
\][/tex]
Substituting the calculated distance:
[tex]\[
\text{Fraction of distance} = \frac{3}{5} \times 15
\][/tex]
[tex]\[
\text{Fraction of distance} = 9
\][/tex]
3. Find the location of the point by starting at [tex]\(A\)[/tex] and moving this fraction of the distance towards [tex]\(B\)[/tex]:
[tex]\[
\text{Location of the point} = A + \text{Fraction of distance}
\][/tex]
Substituting [tex]\(A\)[/tex] and the calculated fraction of distance:
[tex]\[
\text{Location of the point} = 2 + 9 = 11
\][/tex]
Thus, the location of the point that is [tex]\(\frac{3}{5}\)[/tex] of the way from [tex]\(A = 2\)[/tex] to [tex]\(B = 17\)[/tex] is [tex]\(11\)[/tex].
The correct answer is:
D. 11
