To determine the location of the point that is [tex]\(\frac{3}{4}\)[/tex] of the way from [tex]\(A = 31\)[/tex] to [tex]\(B = 6\)[/tex] on the number line, we can follow these steps:
1. Identify the coordinates of the points A and B:
- [tex]\(A = 31\)[/tex]
- [tex]\(B = 6\)[/tex]
2. Calculate the distance between A and B on the number line:
- The distance [tex]\(d\)[/tex] between [tex]\(A\)[/tex] and [tex]\(B\)[/tex] is [tex]\(B - A\)[/tex].
- [tex]\(d = 6 - 31 = -25\)[/tex]
3. Determine the fraction of the distance to travel from A towards B:
- We need to find the point that is [tex]\(\frac{3}{4}\)[/tex] of the way from [tex]\(A\)[/tex] to [tex]\(B\)[/tex].
- The fraction is [tex]\(\frac{3}{4}\)[/tex].
4. Calculate the fraction of the distance:
- Multiply the total distance by the fraction: [tex]\(\frac{3}{4} \times (-25) = -18.75\)[/tex].
5. Calculate the final coordinate:
- Starting from [tex]\(A\)[/tex], we move this distance towards [tex]\(B\)[/tex].
- Final coordinate = [tex]\(A + (-18.75)\)[/tex]
- [tex]\(31 + (-18.75) = 31 - 18.75 = 12.25\)[/tex]
Thus, the location of the point that is [tex]\(\frac{3}{4}\)[/tex] of the way from [tex]\(A = 31\)[/tex] to [tex]\(B = 6\)[/tex] on the number line is [tex]\(12.25\)[/tex].
Since none of the given options match [tex]\(12.25\)[/tex] exactly, it seems there might have been a misunderstanding in the question or the provided choices. Based on our calculation, the correct numerical answer is 12.25. If any discrepancy exists, please double-check the choices given or the exact formulation of the question.
