Midpoint Formula: Deriving & Understanding

  • Context: High School 
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SUMMARY

The discussion focuses on deriving the midpoint and centroid of a triangle using specific vertex coordinates. The centroid of a triangle with vertices A(-a, b), B(a, b), and C(0, 0) is calculated by averaging the coordinates, resulting in the formula (0, (2/3)b). This method is effective for triangles but does not apply to polygons with more than three sides. The conversation highlights the importance of understanding geometric properties when calculating centroids.

PREREQUISITES
  • Understanding of basic geometry concepts, particularly triangles
  • Familiarity with coordinate systems and vertex notation
  • Knowledge of averaging techniques in mathematics
  • Ability to differentiate between midpoint and centroid calculations
NEXT STEPS
  • Research the properties of centroids in polygons with more than three sides
  • Learn about the midpoint formula in coordinate geometry
  • Explore applications of centroids in physics and engineering
  • Study advanced geometric concepts such as barycentric coordinates
USEFUL FOR

Students, educators, and professionals in mathematics, geometry, and engineering who seek to deepen their understanding of geometric properties and calculations related to triangles and centroids.

Meepers
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Figured out, thanks.
 

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I need more information. Find the midpoint of what? Do you mean find the centroid of the triangle? Assuming that line AB is horizontal and P is the midpoint of AB, then the centroid is on the line OP.

One very nice method of finding the centroid of a triangle (doesn't work for figures of more than three sides) is to "average" the three vertices. That is, if the vertices of this triangle are A(-a, b), B(a, b), C(0,0) as it appears, then the centroid is a ((-a+a+ 0)/3, ((b+b+0)/3)= (0, (2/3)b).
 
Its okay, I've figured it out, thank you though.
 

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