Silnik Kartezjański 2Dd = √(Δx² + Δy²)
Kalkulator Odległości i Środka Odcinka
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.
Interactive SVG Coordinate GridSimplified Exact RadicalsMidpoint, Slope & Angle
Result updated: Distance is 2radical 13, approximately 7.2111, midpoint is (3, 5).
Kalkulator Odległości i Środka Odcinka
d = √((x₂ - x₁)² + (y₂ - y₁)²) · M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
Punkt 1 (x₁, y₁)
Enter finite coordinate numbers including negatives or decimals.Punkt 2 (x₂, y₂)
Szybkie Przykłady
Dokładna Odległość
2√13
√52
Długość Dziesiętna
7.211103
dx=4, dy=6
Środek Odcinka (M)
(3, 5)
Nachylenie i Kąt
3/2 (56.31°)
Wyprowadzenie z Twierdzenia Pitagorasa
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
Jak Wzór na Odległość Wynika z 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)