Question
What point on the number line is two-fifths of the way from the point −7 to the point 17?
−1.4
2.0
2.6
7.4
−1.4
2.0
2.6
7.4
Answers
GPT-4o mini
To find the point that is two-fifths of the way from -7 to 17 on the number line, we first need to determine the total distance between these two points.
The distance between -7 and 17 can be calculated as follows:
\[
\text{Distance} = 17 - (-7) = 17 + 7 = 24
\]
Next, we find two-fifths of this total distance:
\[
\text{Two-fifths of the distance} = \frac{2}{5} \times 24 = \frac{48}{5} = 9.6
\]
Now, we need to determine the point that is 9.6 units away from -7 in the direction of 17. We do this by adding 9.6 to -7:
\[
\text{Point} = -7 + 9.6 = 2.6
\]
Therefore, the point on the number line that is two-fifths of the way from -7 to 17 is
\[
\boxed{2.6}
\]
The distance between -7 and 17 can be calculated as follows:
\[
\text{Distance} = 17 - (-7) = 17 + 7 = 24
\]
Next, we find two-fifths of this total distance:
\[
\text{Two-fifths of the distance} = \frac{2}{5} \times 24 = \frac{48}{5} = 9.6
\]
Now, we need to determine the point that is 9.6 units away from -7 in the direction of 17. We do this by adding 9.6 to -7:
\[
\text{Point} = -7 + 9.6 = 2.6
\]
Therefore, the point on the number line that is two-fifths of the way from -7 to 17 is
\[
\boxed{2.6}
\]