📍 平面两点距离计算器（精确根式、中点、斜率、方位角）2D Distance Calculator (Exact Radical, Midpoint, Slope, Bearing)
计算平面上两点 (x₁, y₁)、(x₂, y₂) 的距离 d = √((x₂ − x₁)² + (y₂ − y₁)²)，整数坐标时给出化简根式（如 2√5），同时给出 Δx、Δy、中点、斜率和方向角。本地处理。Distance between two points (x₁, y₁) and (x₂, y₂) in the plane, d = √((x₂ − x₁)² + (y₂ − y₁)²), as a simplified radical for integer coordinates (e.g. 2√5), plus Δx, Δy, midpoint, slope and direction angle. Processed locally.
使用说明与常见问题How-to & FAQ
「平面两点距离计算器（精确根式、中点、斜率、方位角）」是什么？What is the 2D Distance Calculator (Exact Radical, Midpoint, Slope, Bearing) tool?
计算平面上两点 (x₁, y₁)、(x₂, y₂) 的距离 d = √((x₂ − x₁)² + (y₂ − y₁)²)，整数坐标时给出化简根式（如 2√5），同时给出 Δx、Δy、中点、斜率和方向角。本地处理。Distance between two points (x₁, y₁) and (x₂, y₂) in the plane, d = √((x₂ − x₁)² + (y₂ − y₁)²), as a simplified radical for integer coordinates (e.g. 2√5), plus Δx, Δy, midpoint, slope and direction angle. Processed locally.
如何使用「平面两点距离计算器（精确根式、中点、斜率、方位角）」？How do I use the 2D Distance Calculator (Exact Radical, Midpoint, Slope, Bearing) tool?
在「平面两点距离计算器（精确根式、中点、斜率、方位角）」中，填写「x₁」、「y₁」、「x₂」、「y₂」等参数，结果会随输入实时计算并显示在下方。In the 2D Distance Calculator (Exact Radical, Midpoint, Slope, Bearing): Fill in "x₁", "y₁", "x₂", "y₂"; results are recalculated instantly as you type.
两点距离公式是什么？What is the distance formula?
d = √((x₂ − x₁)² + (y₂ − y₁)²)，就是以 Δx、Δy 为直角边的直角三角形的斜边（勾股定理）。(1, 2) 到 (5, −6)：√(16 + 64) = √80 = 4√5 ≈ 8.944。d = √((x₂ − x₁)² + (y₂ − y₁)²), the hypotenuse of the right triangle with legs Δx and Δy (Pythagoras). From (1, 2) to (5, −6): √(16 + 64) = √80 = 4√5 ≈ 8.944.
能举个计算实例吗？Can you show a worked example?
例如在「平面两点距离计算器（精确根式、中点、斜率、方位角）」中填 x₁ = 1，y₁ = 2，x₂ = 5，y₂ = -6，结果区显示：距离：8.94427191 = 4√5；Δx, Δy：4, −8；中点：(3, −2)；斜率：−2；方向角（从 +x 轴逆时针）：296.565051°；ℹ d = √(Δx² + Δy²)For example, entering x₁ = 1, y₁ = 2, x₂ = 5, y₂ = -6 in the 2D Distance Calculator (Exact Radical, Midpoint, Slope, Bearing) gives: Distance: 8.94427191 = 4√5; Δx, Δy: 4, −8; Midpoint: (3, −2); Slope: −2; Direction angle (counter-clockwise from +x): 296.565051°; ℹ d = √(Δx² + Δy²)
哪些输入会被检查？Which inputs are validated?
「平面两点距离计算器（精确根式、中点、斜率、方位角）」会检查这些输入——「x₁」：须为数字；「y₁」：必须填写，须为数字；「x₂」：必须填写，须为数字；「y₂」：必须填写，须为数字；绝对值超过 10¹⁵ 的数也会被拒绝。不符合时结果区显示具体提示，不会给出数字。The 2D Distance Calculator (Exact Radical, Midpoint, Slope, Bearing) checks its inputs — "x₁": must be a number; "y₁": required, must be a number; "x₂": required, must be a number; "y₂": required, must be a number; numbers above 10¹⁵ in absolute value are rejected too. When a value fails, the result area names the problem instead of showing a number.
有哪些选项可以调整？What options can I adjust?
「平面两点距离计算器（精确根式、中点、斜率、方位角）」的设置：「x₁」默认 1；「y₁」默认 2；「x₂」默认 5；「y₂」默认 -6。每次生成结果都按当前设置处理。Settings in the 2D Distance Calculator (Exact Radical, Midpoint, Slope, Bearing) — "x₁" default 1; "y₁" default 2; "x₂" default 5; "y₂" default -6. The result always uses the current settings.
计算精度如何？How precise are the results?
「平面两点距离计算器（精确根式、中点、斜率、方位角）」使用 JavaScript 双精度浮点数（约 15–16 位有效数字）；极大或极小的数值可能存在精度误差。The 2D Distance Calculator (Exact Radical, Midpoint, Slope, Bearing) uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「平面两点距离计算器（精确根式、中点、斜率、方位角）」免费吗？需要注册吗？Is the 2D Distance Calculator (Exact Radical, Midpoint, Slope, Bearing) free? Do I need an account?
「平面两点距离计算器（精确根式、中点、斜率、方位角）」完全免费，无需注册或安装，打开网页即可使用，手机和电脑都能用；输入的内容只在你的浏览器本地处理。The 2D Distance Calculator (Exact Radical, Midpoint, Slope, Bearing) is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.