Math Problem Statement
Find the midpoint of the segment with the following endpoints.
left parenthesis, 2, comma, 10, right parenthesis, and , left parenthesis, minus, 8, comma, 7, right parenthesis
(2,10) and (−8,7)
Solution
To find the midpoint of the segment with endpoints and , we use the midpoint formula:
Given:
- ,
- ,
Substitute these values into the formula:
Simplify each part:
Thus, the midpoint of the segment is .
Would you like further details or have any questions?
Here are some related questions you might find useful:
- How do you determine the equation of a line given two endpoints?
- How can the midpoint formula be used in three dimensions?
- What is the distance between the midpoint and one of the endpoints?
- How does the midpoint relate to the centroid of a triangle?
- Can the midpoint formula be used in geometry problems involving circles?
Tip: The midpoint is always equidistant from both endpoints, making it a valuable tool in various geometric constructions and proofs.
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Math Problem Analysis
Mathematical Concepts
Coordinate Geometry
Midpoint Formula
Formulas
Midpoint formula: \( \left( \frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2} \right) \)
Theorems
-
Suitable Grade Level
Grades 8-10