／／ 平行与垂直线Parallel and Perpendicular Lines
由斜率得平行/垂直斜率。本地处理。可设置「已知斜率」。Parallel/perpendicular slopes from a given slope. Processed locally. Settings: Slope.
使用说明与常见问题How-to & FAQ
「平行与垂直线」是什么？What is the Parallel and Perpendicular Lines tool?
由斜率得平行/垂直斜率。本地处理。可设置「已知斜率」。Parallel/perpendicular slopes from a given slope. Processed locally. Settings: Slope.
如何使用「平行与垂直线」？How do I use the Parallel and Perpendicular Lines tool?
在「平行与垂直线」中，填写「已知斜率」等参数，结果会随输入实时计算并显示在下方。In the Parallel and Perpendicular Lines: Fill in "Slope"; results are recalculated instantly as you type.
会给出直线方程吗？Does it give line equations?
不会，只给斜率：平行线斜率与原斜率相同，垂直线斜率为 −1/m；原斜率为 0 时垂直线是竖直线，斜率不存在。要写方程，可代入点斜式 y − y₁ = m(x − x₁)。No, only the slopes: a parallel line has the same slope and a perpendicular one has −1/m; if the slope is 0, the perpendicular is vertical and has no slope. For an equation, use point-slope form y − y₁ = m(x − x₁).
能举个计算实例吗？Can you show a worked example?
例如在「平行与垂直线」中填 已知斜率 = 2，结果区显示：平行线斜率：2；垂直线斜率：-0.5For example, entering Slope = 2 in the Parallel and Perpendicular Lines gives: Parallel slope: 2; Perpendicular slope: -0.5
哪些输入会被检查？Which inputs are validated?
「平行与垂直线」会检查这些输入——「已知斜率」：必须填写；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 Parallel and Perpendicular Lines checks its inputs — "Slope": required; 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?
「平行与垂直线」的设置：「已知斜率」默认 2。每次生成结果都按当前设置处理。Settings in the Parallel and Perpendicular Lines — "Slope" default 2. The result always uses the current settings.
计算精度如何？How precise are the results?
「平行与垂直线」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 Parallel and Perpendicular Lines uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「平行与垂直线」免费吗？需要注册吗？Is the Parallel and Perpendicular Lines free? Do I need an account?
「平行与垂直线」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 Parallel and Perpendicular Lines is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.