Jak vypočítat Midpoint
Co je Midpoint?
The midpoint is the exact centre point between two given points. It divides the line segment into two equal halves. Used in geometry, coordinate systems, and navigation.
Vzorec
M = ((x₁ + x₂)/2, (y₁ + y₂)/2) in 2D; M = ((x₁ + x₂)/2, (y₁ + y₂)/2, (z₁ + z₂)/2) in 3D
- P₁
- first point
- P₂
- second point
- M
- midpoint between P₁ and P₂
Průvodce krok za krokem
- 1Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2)
- 2Average the x-coordinates and y-coordinates separately
- 3Distance from either endpoint is the same
- 4Extends to 3D: add z-coordinates similarly
Worked Examples
Vstup
(2,4) and (8,6)
Výsledek
Midpoint = ((2+8)/2, (4+6)/2) = (5, 5)
Vstup
(−3,7) and (5,1)
Výsledek
Midpoint = (1, 4)
Frequently Asked Questions
Is the midpoint always exactly in the middle?
Yes, it divides the segment into two equal parts: d(P₁, M) = d(M, P₂).
Can I use the midpoint formula in reverse (find endpoint)?
Yes, if you know midpoint M and one endpoint P₁, find P₂ = 2M − P₁.
How is the midpoint related to the circumcenter?
For a right triangle, the midpoint of the hypotenuse is the circumcenter (center of circumcircle).
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