Answer :
Sure! Let's work through the problem step by step to find the location of the point on the number line that is [tex]\(\frac{2}{7}\)[/tex] of the way from [tex]\(A = 18\)[/tex] to [tex]\(B = 4\)[/tex].
1. Identify the positions of points A and B:
- [tex]\(A = 18\)[/tex]
- [tex]\(B = 4\)[/tex]
2. Calculate the distance from point A to point B:
[tex]\[ \text{Distance} = B - A = 4 - 18 = -14 \][/tex]
The distance is [tex]\(-14\)[/tex].
3. Determine the fraction of the distance:
We want to find the position that is [tex]\(\frac{2}{7}\)[/tex] of the way from [tex]\(A\)[/tex] to [tex]\(B\)[/tex].
4. Calculate the location of the point that is [tex]\(\frac{2}{7}\)[/tex] of the way from [tex]\(A\)[/tex] to [tex]\(B\)[/tex]:
[tex]\[ \text{Point Location} = A + \left( \frac{2}{7} \right) \times \text{Distance} = 18 + \left( \frac{2}{7} \right) \times (-14) \][/tex]
5. Simplify the expression:
[tex]\[ \text{Point Location} = 18 + \left( \frac{2}{7} \times -14 \right) \][/tex]
[tex]\[ \text{Point Location} = 18 + \left( \frac{2 \times (-14)}{7} \right) \][/tex]
[tex]\[ \text{Point Location} = 18 + \left( \frac{-28}{7} \right) \][/tex]
[tex]\[ \text{Point Location} = 18 + (-4) \][/tex]
[tex]\[ \text{Point Location} = 18 - 4 = 14 \][/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:
[tex]\[ \boxed{14} \][/tex]
1. Identify the positions of points A and B:
- [tex]\(A = 18\)[/tex]
- [tex]\(B = 4\)[/tex]
2. Calculate the distance from point A to point B:
[tex]\[ \text{Distance} = B - A = 4 - 18 = -14 \][/tex]
The distance is [tex]\(-14\)[/tex].
3. Determine the fraction of the distance:
We want to find the position that is [tex]\(\frac{2}{7}\)[/tex] of the way from [tex]\(A\)[/tex] to [tex]\(B\)[/tex].
4. Calculate the location of the point that is [tex]\(\frac{2}{7}\)[/tex] of the way from [tex]\(A\)[/tex] to [tex]\(B\)[/tex]:
[tex]\[ \text{Point Location} = A + \left( \frac{2}{7} \right) \times \text{Distance} = 18 + \left( \frac{2}{7} \right) \times (-14) \][/tex]
5. Simplify the expression:
[tex]\[ \text{Point Location} = 18 + \left( \frac{2}{7} \times -14 \right) \][/tex]
[tex]\[ \text{Point Location} = 18 + \left( \frac{2 \times (-14)}{7} \right) \][/tex]
[tex]\[ \text{Point Location} = 18 + \left( \frac{-28}{7} \right) \][/tex]
[tex]\[ \text{Point Location} = 18 + (-4) \][/tex]
[tex]\[ \text{Point Location} = 18 - 4 = 14 \][/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:
[tex]\[ \boxed{14} \][/tex]
