🔺 三角形重心Triangle Centroid Calculator
重心 G = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3)，是三条中线的交点；同时给出面积。本地处理。Centroid G = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3), where the three medians meet; the area is shown too. Processed locally.
使用说明与常见问题How-to & FAQ
「三角形重心」是什么？What is the Triangle Centroid Calculator tool?
重心 G = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3)，是三条中线的交点；同时给出面积。本地处理。Centroid G = ((x₁ + x₂ + x₃)/3, (y₁ + y₂ + y₃)/3), where the three medians meet; the area is shown too. Processed locally.
如何使用「三角形重心」？How do I use the Triangle Centroid Calculator tool?
填写三个顶点的坐标 x₁、y₁、x₂、y₂、x₃、y₃，即可得到重心坐标和三角形面积。结果会随输入实时更新。Enter the vertices x₁, y₁, x₂, y₂, x₃ and y₃ to get the centroid and the triangle's area. The result updates as you type.
物理意义？Physical meaning?
均匀薄板三角形的质心就在重心处，可以在这一点把它平衡住。A uniform triangular plate balances on its centroid.
能举个计算实例吗？Can you show a worked example?
例如在「三角形重心」中填 x₁ = 0，y₁ = 0，x₂ = 6，y₂ = 0，x₃ = 0，y₃ = 9，结果区显示：重心 G：(2, 3)；面积：27For example, entering x₁ = 0, y₁ = 0, x₂ = 6, y₂ = 0, x₃ = 0, y₃ = 9 in the Triangle Centroid Calculator gives: Centroid G: (2, 3); Area: 27
哪些输入会被检查？Which inputs are validated?
「三角形重心」会检查这些输入——「x₁」、「y₁」、「x₂」、「y₂」、「x₃」、「y₃」：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 Triangle Centroid Calculator checks its inputs — "x₁", "y₁", "x₂", "y₂", "x₃", "y₃": 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?
「三角形重心」的设置：「x₁」默认 0；「y₁」默认 0；「x₂」默认 6；「y₂」默认 0；「x₃」默认 0；「y₃」默认 9。每次生成结果都按当前设置处理。Settings in the Triangle Centroid Calculator — "x₁" default 0; "y₁" default 0; "x₂" default 6; "y₂" default 0; "x₃" default 0; "y₃" default 9. The result always uses the current settings.
计算精度如何？How precise are the results?
「三角形重心」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 Triangle Centroid Calculator uses double-precision floating point (about 15–16 significant digits); very large or very small values may lose precision.
「三角形重心」免费吗？需要注册吗？Is the Triangle Centroid Calculator free? Do I need an account?
「三角形重心」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 Triangle Centroid Calculator is completely free with no sign-up or install and works on phones and desktops; what you enter is processed only in your browser.