2D декартова геометрияd = √(Δx² + Δy²)
Калькулятор расстояния по координатам
Plot any two points (x₁, y₁) and (x₂, y₂) on the Cartesian plane to compute exact radical distance, midpoint, slope, and inclination angle. Looking for standard triangle side lengths or inverse trigonometry? Visit our root Pythagoras equation solver.
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Result updated: Distance is 2radical 13, approximately 7.2111, midpoint is (3, 5).
Калькулятор расстояния по координатам
d = √((x₂ - x₁)² + (y₂ - y₁)²) · M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Точка 1 (x₁, y₁)
Enter finite coordinate numbers including negatives or decimals.Точка 2 (x₂, y₂)
Быстрые примеры
Точное расстояние
2√13
√52
Десятичная длина
7.211103
dx=4, dy=6
Середина отрезка (M)
(3, 5)
Уклон и угол наклона
3/2 (56.31°)
Вывод через теорему Пифагора
1. Map Horizontal & Vertical Leg Lengths (dx, dy)
dx = |5 - 1| = 4, dy = |8 - 2| = 6
a = 4, b = 6
2. Apply the Pythagorean Sum of Squares
d² = 4² + 6²
d² = 16 + 36 = 52
3. Extract Exact Radical & Decimal Hypotenuse
d = √52
d = 2√13 ≈ 7.2111
4. Compute Midpoint & Slope
M = ((1 + 5)/2, (2 + 8)/2)
M = (3, 5), m = 3/2
Как формула расстояния сводится к a² + b² = c²
Every non-vertical, non-horizontal segment between two points forms the hypotenuse c of an invisible right triangle whose horizontal run is a = dx = |x₂ - x₁| and whose vertical rise is b = dy = |y₂ - y₁|.
a² + b² = c² ⟹ (|x₂ - x₁|)² + (|y₂ - y₁|)² = d² ⟹ d = √((x₂ - x₁)² + (y₂ - y₁)²)