平面几何

复制import math

# 两点距离
def distance(p1, p2):
    return math.hypot(p2[0] - p1[0], p2[1] - p1[1])

# 直线方程（一般式 Ax + By + C = 0）
def line_from_points(p1, p2):
    A = p2[1] - p1[1]
    B = p1[0] - p2[0]
    C = p2[0] * p1[1] - p1[0] * p2[1]
    return A, B, C

# 点到直线距离
def point_to_line_distance(point, line):
    A, B, C = line
    x, y = point
    return abs(A * x + B * y + C) / math.hypot(A, B)

# 示例
p1, p2 = (1, 2), (4, 6)
print(f"两点距离: {distance(p1, p2)}")  # 5.0
line = line_from_points(p1, p2)
print(f"直线方程: {line[0]}x + {line[1]}y + {line[2]} = 0")  # 4x + -3y + 2 = 0
print(f"点到直线距离: {point_to_line_distance((0, 0), line)}")  # 0.4

复制package main

import (
	"fmt"
	"math"
)

type Point struct{ X, Y float64 }
type Line struct{ A, B, C float64 }

func distance(p1, p2 Point) float64 {
	dx, dy := p2.X-p1.X, p2.Y-p1.Y
	return math.Sqrt(dx*dx + dy*dy)
}

func lineFromPoints(p1, p2 Point) Line {
	return Line{
		A: p2.Y - p1.Y,
		B: p1.X - p2.X,
		C: p2.X*p1.Y - p1.X*p2.Y,
	}
}

func pointToLineDistance(p Point, l Line) float64 {
	return math.Abs(l.A*p.X+l.B*p.Y+l.C) / math.Sqrt(l.A*l.A+l.B*l.B)
}

func main() {
	p1, p2 := Point{1, 2}, Point{4, 6}
	fmt.Printf("两点距离: %.1f\n", distance(p1, p2)) // 5.0
	line := lineFromPoints(p1, p2)
	fmt.Printf("直线方程: %.0fx + %.0fy + %.0f = 0\n", line.A, line.B, line.C)
	fmt.Printf("点到直线距离: %.1f\n", pointToLineDistance(Point{0, 0}, line)) // 0.4
}

复制// 两点距离
const distance = ([x1, y1], [x2, y2]) =>
  Math.hypot(x2 - x1, y2 - y1);

// 直线方程（一般式 Ax + By + C = 0）
const lineFromPoints = ([x1, y1], [x2, y2]) => {
  const A = y2 - y1;
  const B = x1 - x2;
  const C = x2 * y1 - x1 * y2;
  return { A, B, C };
};

// 点到直线距离
const pointToLineDistance = ([x, y], { A, B, C }) =>
  Math.abs(A * x + B * y + C) / Math.hypot(A, B);

// 示例
const p1 = [1, 2], p2 = [4, 6];
console.log(`两点距离: ${distance(p1, p2)}`); // 5.0
const line = lineFromPoints(p1, p2);
console.log(`直线方程: ${line.A}x + ${line.B}y + ${line.C} = 0`);
console.log(`点到直线距离: ${pointToLineDistance([0, 0], line)}`); // 0.4