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], follow these steps:
1. Determine the distance between the two points:
The distance between points [tex]\(A\)[/tex] and [tex]\(B\)[/tex] is calculated by subtracting the coordinate of point [tex]\(A\)[/tex] from the coordinate of point [tex]\(B\)[/tex]:
[tex]\[
\text{Distance} = B - A = 17 - 2 = 15
\][/tex]
2. Calculate [tex]\(\frac{3}{5}\)[/tex] of the distance:
To find [tex]\(\frac{3}{5}\)[/tex] of the distance, multiply the total distance by [tex]\(\frac{3}{5}\)[/tex]:
[tex]\[
\frac{3}{5} \text{ of the distance} = \frac{3}{5} \times 15 = 9.0
\][/tex]
3. Find the location that is [tex]\(\frac{3}{5}\)[/tex] of the way from [tex]\(A\)[/tex] to [tex]\(B\)[/tex]:
Starting from point [tex]\(A\)[/tex], add the result from the previous step to the coordinate of point [tex]\(A\)[/tex]:
[tex]\[
\text{Location} = A + \frac{3}{5} \text{ of the distance} = 2 + 9 = 11
\][/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 [tex]\(\boxed{11}\)[/tex].
