2D 데카르트 거리 엔진d = √(Δx² + Δy²)
좌표 거리 및 중점 계산기
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).
좌표 거리 및 중점 계산기
d = √((x₂ - x₁)² + (y₂ - y₁)²) · M = ((x₁ + x₂)/2, (y₁ + y₂)/2)
점 1 (x₁, y₁)
Enter finite coordinate numbers including negatives or decimals.점 2 (x₂, y₂)
빠른 좌표 예시
정확한 거리
2√13
√52
소수 길이
7.211103
dx=4, dy=6
중점 (M)
(3, 5)
기울기 및 경사각
3/2 (56.31°)
피타고라스 거리 유도
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
거리 공식과 a² + b² = c² 의 연결 원리
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)