Math Problem Statement
Find the missing endpoint of a segment with one endpoint at (-8, -5) and the midpoint at (2, 3).
Solution
To find the missing endpoint of a segment when one endpoint and the midpoint are given, we can use the midpoint formula:
Given:
- One endpoint
- Midpoint
- Missing endpoint
We can set up the following system of equations based on the midpoint formula:
Solving for :
Multiply both sides by 2: Solve for :
Solving for :
Multiply both sides by 2: Solve for :
Thus, the missing endpoint is .
The correct answer is .
Would you like any further clarification or details on how this was calculated?
Here are 5 related questions:
- How do you calculate the midpoint if both endpoints are known?
- How does the midpoint formula apply in 3D geometry?
- What is the significance of a midpoint in dividing a line segment?
- Can the midpoint formula be used for weighted averages in statistics?
- How would you find the midpoint if one endpoint and the midpoint are fractions?
Tip: Always double-check your calculations, especially when solving for unknowns, to avoid simple arithmetic mistakes!
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Midpoint Formula
Linear Equations
Formulas
Midpoint Formula: M = ((x1 + x2) / 2, (y1 + y2) / 2)
Theorems
-
Suitable Grade Level
Grades 8-10