Math Problem Statement
solve
Solution
We are given two points, and , on a number line, with the following information:
- The distance between and is 5 units, i.e., .
- is located at .
We need to find the possible location(s) of .
Solution:
The distance between and is 5, which means that could be either 5 units to the left or 5 units to the right of .
This gives two possible equations:
Since , we substitute that into both equations:
Thus, the two possible locations of are and .
Final answer:
The possible locations of are and .
Would you like any further details or clarifications?
Related Questions:
- What happens if the distance between two points on a number line is given as a variable instead of a number?
- How would this problem change if point was given as a positive number?
- Can you derive a general formula to find the location of one point given the distance from another point?
- How do you interpret negative distances in real-world scenarios involving a number line?
- How can this problem be visualized geometrically?
Tip:
Always consider both directions when given a distance on a number line to account for all possible locations of the second point.
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Math Problem Analysis
Mathematical Concepts
Number Line
Distance on a Number Line
Formulas
E = F - Distance
E = F + Distance
Theorems
Concept of distance between points on a number line
Suitable Grade Level
Grades 6-8