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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.
الصيغة
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
دليل خطوة بخطوة
- 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
أمثلة محلولة
الإدخال
(2,4) and (8,6)
النتيجة
Midpoint = ((2+8)/2, (4+6)/2) = (5, 5)
الإدخال
(−3,7) and (5,1)
النتيجة
Midpoint = (1, 4)
أسئلة شائعة
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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