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What point on the number line is [tex]\frac{2}{5}[/tex] of the way from the point [tex]-7[/tex] to the point [tex]17[/tex]?

A. [tex]-1.4[/tex]
B. [tex]2.0[/tex]
C. [tex]2.6[/tex]
D. [tex]7.4[/tex]


Sagot :

Certainly! Let's approach this problem step-by-step.

1. Identify the two points on the number line:
- The first point, [tex]\( \text{point1} \)[/tex], is [tex]\(-7\)[/tex].
- The second point, [tex]\( \text{point2} \)[/tex], is [tex]\(17\)[/tex].

2. Find the distance between the two points:
[tex]\[ \text{Distance} = \text{point2} - \text{point1} = 17 - (-7) = 17 + 7 = 24 \][/tex]
So, the distance between the points [tex]\(-7\)[/tex] and [tex]\(17\)[/tex] is [tex]\(24\)[/tex].

3. Calculate the fraction of the way:
We need to determine the point that is [tex]\(\frac{2}{5}\)[/tex] of the way from [tex]\(-7\)[/tex] to [tex]\(17\)[/tex].

4. Calculate the actual distance corresponding to this fraction:
[tex]\[ \text{Fractional distance} = \text{Distance} \times \frac{2}{5} = 24 \times \frac{2}{5} = 24 \times 0.4 = 9.6 \][/tex]

5. Find the coordinate of the point [tex]\(\frac{2}{5}\)[/tex] of the way from [tex]\(-7\)[/tex] to [tex]\(17\)[/tex]:
Start from [tex]\(-7\)[/tex] and move [tex]\(9.6\)[/tex] units towards [tex]\(17\)[/tex].

[tex]\[ \text{Point} = \text{point1} + \text{Fractional distance} = -7 + 9.6 = 2.6 \][/tex]

Therefore, the point on the number line that is [tex]\(\frac{2}{5}\)[/tex] of the way from [tex]\(-7\)[/tex] to [tex]\(17\)[/tex] is [tex]\(2.6\)[/tex].

So, the correct answer is [tex]\(2.6\)[/tex].
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