{"id":6973,"date":"2025-12-24T17:19:41","date_gmt":"2025-12-24T08:19:41","guid":{"rendered":"https:\/\/math-travel.com\/?p=6973"},"modified":"2026-02-11T16:40:54","modified_gmt":"2026-02-11T07:40:54","slug":"2point-distance","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-2\/2point-distance\/","title":{"rendered":"2\u70b9\u9593\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u308b\u516c\u5f0f\uff1a\u5e73\u9762\u30fb\u7a7a\u9593\u3069\u3061\u3089\u3082\u4f7f\u3048\u308b\u8a08\u7b97\u65b9\u6cd5\u3092\u4f8b\u984c\u3067\u30c1\u30a7\u30c3\u30af"},"content":{"rendered":"\n

\u300c2\u70b9\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u305f\u3044\u300d<\/span>
\u300c2\u70b9\u9593\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u308b\u516c\u5f0f\u3092\u5fd8\u308c\u305f\u300d<\/span>
\u4eca\u56de\u306f\u3053\u3093\u306a\u60a9\u307f\u3092\u89e3\u6c7a\u3057\u3066\u3044\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n

\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u8ddd\u96e2\u3092\u6c42\u3081\u305f\u3044\u3093\u3060\u3051\u3069\u516c\u5f0f\u3092\u5fd8\u308c\u3061\u3083\u3063\u3066\u2026<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u5e73\u9762\u306b\u304a\u3051\u308b2\u70b9\u9593\u306e\u8ddd\u96e2\u306f\u4ee5\u4e0b\u306e\u516c\u5f0f\u3067\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n

\n
\"2\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u306e\u8a3c\u660e\"<\/figure>\n<\/div>\n\n\n
2\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f<\/span><\/div>
\n

2\u70b9\\(A\\left(x_{1},y_{1}\\right)\\),\\(B\\left(x_{2},y_{2}\\right)\\)\u9593\u306e\u8ddd\u96e2\\(AB\\)\u306f<\/p>\n\n\n\n

\\[AB=\\sqrt{\\left(x_{2}-x_{1}\\right)^{2}+\\left(y_{2}-y_{1}\\right)^{2}}\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u6c7a\u3057\u3066\u96e3\u3057\u3044\u516c\u5f0f\u3067\u306f\u306a\u3044\u306e\u3067\u3001\u4f7f\u3044\u3053\u306a\u305b\u308b\u3088\u3046\u306b\u306a\u308a\u305f\u3044\u516c\u5f0f\u3067\u3059\u3002<\/p>\n\n\n\n

\u672c\u8a18\u4e8b\u3067\u306f2\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u89e3\u8aac<\/span>\u3057\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u5e73\u9762\u3060\u3051\u3067\u306a\u304f\u3001\u7a7a\u9593\u4e0a\u306e2\u70b9\u9593\u306e\u8ddd\u96e2\u306b\u3064\u3044\u3066\u3082\u89e3\u8aac\u3057\u3066\u3044\u308b\u306e\u3067\u3001\u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n

\"\"\u30b7\u30fc\u30bf<\/span><\/div>
\n

\u6c17\u306b\u306a\u308b\u898b\u51fa\u3057\u3092\u30af\u30ea\u30c3\u30af\u3057\u3066\u3001
\u305c\u3072\u6700\u5f8c\u307e\u3067\u3054\u89a7\u304f\u3060\u3055\u3044\u3002<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

2\u70b9\u9593\u306e\u8ddd\u96e2\u3068\u306f\uff1f<\/h2>\n\n\n\n

2\u70b9\u9593\u306e\u8ddd\u96e2\u3068\u306f\u30012\u70b9\\(A,B\\)\u304c\u3042\u308b\u3068\u304d\u306e\u7dda\u5206\\(AB\\)\u306e\u9577\u3055\u3092\u6307\u3057\u307e\u3059\u3002<\/p>\n\n\n

\n
\"2\u70b9\u9593\u306e\u8ddd\u96e2\u3068\u306f\"<\/figure>\n<\/div>\n\n\n

\u8ddd\u96e2\u3068\u306f\u6700\u77ed\u7d4c\u8def\u306a\u306e\u3067\u3001\u66f2\u7dda\u3067\u306f\u306a\u304f\u76f4\u7dda<\/span>\u3067\u3064\u306a\u3044\u3067\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n

2\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f<\/h2>\n\n\n\n

2\u70b9\u9593\u306e\u8ddd\u96e2\u306f\u4ee5\u4e0b\u306e\u516c\u5f0f\u3067\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/span><\/p>\n\n\n\n

2\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f<\/span><\/div>
\n

2\u70b9\\(A\\left(x_{1},y_{1}\\right)\\),\\(B\\left(x_{2},y_{2}\\right)\\)\u9593\u306e\u8ddd\u96e2\\(AB\\)\u306f<\/p>\n\n\n\n

\\[AB=\\sqrt{\\left(x_{2}-x_{1}\\right)^{2}+\\left(y_{2}-y_{1}\\right)^{2}}\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u5177\u4f53\u4f8b\u3092\u3082\u3068\u306b2\u70b9\u9593\u306e\u8ddd\u96e2\u3092\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

2\u70b9\\(A\\left(1,2\\right)\\),\\(B\\left(5,5\\right)\\)\u304c\u3042\u308b\u3068\u304d\u3001\u305d\u306e\u8ddd\u96e2\\(AB\\)\u306f<\/p>\n\n\n

\n
\"2\u70b9\u9593\u306e\u8ddd\u96e2\"<\/figure>\n<\/div>\n\n\n

\\begin{eqnarray}
AB&=&\\sqrt{\\left(5-1\\right)^{2}+\\left(5-2\\right)^{2}}\\\\
&=&\\sqrt{4^{2}+3^{2}}\\\\
&=&\\sqrt{25}\\\\
&=&5
\\end{eqnarray}<\/p>\n\n\n\n

\u3053\u308c\u30672\u70b9\\(A,B\\)\u9593\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u8ddd\u96e2\u306e\u516c\u5f0f\u306e\u8a3c\u660e<\/h2>\n\n\n\n

\u306a\u305c2\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u304c\u6210\u308a\u7acb\u3064\u306e\u304b\u8003\u3048\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u3069\u306e\u516c\u5f0f\u3067\u3082\u516c\u5f0f\u306e\u4ed5\u7d44\u307f\u3092\u7406\u89e3\u3057\u3066\u304a\u304f\u3068\u899a\u3048\u3084\u3059\u3044\u3067\u3059\u3002<\/p>\n\n\n\n

2\u70b9\\(A\\left(x_{1},y_{1}\\right)\\),\\(B\\left(x_{2},y_{2}\\right)\\)\u3068\u3059\u308b\u3068\u3001\u4e0b\u306e\u56f3\u306e\u76f4\u89d2\u4e09\u89d2\u5f62ABC\u3092\u63cf\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n

\n
\"2\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u306e\u8a3c\u660e\"<\/figure>\n<\/div>\n\n\n

\u4e09\u5e73\u65b9\u306e\u5b9a\u7406\u3088\u308a<\/p>\n\n\n\n

\\[AB^{2}=AC^{2}+BC^{2}\\]<\/p>\n\n\n\n

\u304c\u6210\u308a\u7acb\u3064\u306e\u3067<\/p>\n\n\n\n

\\[AB^{2}=\\left(x_{2}-x_{1}\\right)^{2}+\\left(y_{2}-y_{1}\\right)^{2}\\]<\/p>\n\n\n\n

\u3068\u306a\u308a\u307e\u3059\u3002<\/p>\n\n\n\n

\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n

\\[AB=\\sqrt{\\left(x_{2}-x_{1}\\right)^{2}+\\left(y_{2}-y_{1}\\right)^{2}}\\]<\/span><\/p>\n\n\n

\n
\"2\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u306e\u8a3c\u660e\"<\/figure>\n<\/div>\n\n
\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u4e2d\u5b66\u6821\u3067\u7fd2\u3063\u305f\u4e09\u5e73\u65b9\u306e\u5b9a\u7406\u3092\u6d3b\u7528\u3057\u3066\u3044\u308b\u3093\u3067\u3059\u306d\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

3\u6b21\u5143\u306b\u304a\u3051\u308b2\u70b9\u9593\u306e\u8ddd\u96e2<\/h2>\n\n\n\n

\u3053\u3053\u307e\u3067\u306f\\(xy\\)\u5e73\u9762\u306e2\u6b21\u5143\u306b\u304a\u3051\u308b\u8ddd\u96e2\\(AB\\)\u3092\u8003\u3048\u3066\u304d\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u6b21\u306f3\u6b21\u5143\u306b\u304a\u3051\u308b2\u70b9\u9593\u306e\u8ddd\u96e2<\/span>\u3092\u6c42\u3081\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n

\u7a7a\u9593\u4e0a\u306e2\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f<\/span><\/div>
\n

2\u70b9\\(A\\left(x_{1},y_{1},z_{1}\\right)\\),\\(B\\left(x_{2},y_{2},z_{2}\\right)\\)\u9593\u306e\u8ddd\u96e2\\(AB\\)\u306f<\/p>\n\n\n\n

\\[AB=\\sqrt{\\left(x_{2}-x_{1}\\right)^{2}+\\left(y_{2}-y_{1}\\right)^{2}+\\left(z_{2}-z_{1}\\right)^{2}}\\]<\/p>\n<\/div><\/div>\n\n\n\n

\u7a7a\u9593\u4e0a\u306e2\u70b9\\(A\\left(1,2,2\\right)\\),\\(B\\left(4,5,5\\right)\\)\u9593\u306e\u8ddd\u96e2\\(AB\\)\u306f<\/p>\n\n\n\n

\\begin{eqnarray}
AB&=&\\sqrt{\\left(4-1\\right)^{2}+\\left(5-2\\right)^{2}+\\left(5-2\\right)^{2}}\\\\
&=&\\sqrt{3^{2}+3^{2}+3^{2}}\\\\
&=&\\sqrt{27}\\\\
&=&3\\sqrt{3}
\\end{eqnarray}<\/p>\n\n\n\n

3\u6b21\u5143\u306b\u306a\u308b\u3068\u5ea7\u6a19\u304c1\u3064\u5897\u3048\u307e\u3057\u305f\u306d\u3002<\/p>\n\n\n\n

\u3057\u304b\u3057\u30013\u6b21\u5143\u3067\u3082\u516c\u5f0f\u306e\u4f7f\u3044\u65b9\u306f2\u6b21\u5143\u3068\u5909\u308f\u3089\u306a\u3044\u306e\u3067\u7c21\u5358\u3067\u3059\u3002<\/p>\n\n\n

\"\"\u30b7\u30fc\u30bf<\/span><\/div>
\n

3\u6b21\u5143\u306e\u8ddd\u96e2\u3082\u6c42\u3081\u3089\u308c\u308b\u3088\u3046\u306b\u3057\u3066\u304a\u3053\u3046\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u539f\u70b9\u304b\u3089\u306e\u8ddd\u96e2<\/h2>\n\n\n\n

\u539f\u70b9\u304b\u3089\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n

\n
\"\u539f\u70b9\u304b\u3089\u306e\u8ddd\u96e2\"<\/figure>\n<\/div>\n\n\n

\u539f\u70b9\u3092\\(O\\left(0,0\\right)\\)\u3068\u8003\u3048\u3066\u3001\u70b9\\(A\\left(x_{1},y_{1}\\right)\\)\u3068\u306e\u8ddd\u96e2\\(OA\\)\u306f<\/p>\n\n\n\n

\\[OA=\\sqrt{x_{1}^{2}+y_{1}^{2}}\\]<\/p>\n\n\n\n

2\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u8a3c\u660e\u3068\u540c\u69d8\u306b\u3001\u4e09\u5e73\u65b9\u306e\u5b9a\u7406\u3092\u8003\u3048\u308c\u3070\u7d0d\u5f97\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002<\/p>\n\n\n

\n
\"\u539f\u70b9\u304b\u3089\u306e\u8ddd\u96e2\"<\/figure>\n<\/div>\n\n
\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u3053\u308c\u306f\u7c21\u5358\u3067\u3059\u306d\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n

\"\"\u30b7\u30fc\u30bf<\/span><\/div>
\n

\u305d\u3046\u3060\u306d\uff012\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u306b(0,0)\u3092\u4ee3\u5165\u3059\u308c\u3070\u81ea\u7136\u3068\u6c42\u3081\u3089\u308c\u308b\u3088<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

2\u70b9\u9593\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u308b\u300a\u7df4\u7fd2\u554f\u984c\u300b<\/h2>\n\n\n
\n
\"2\u70b9\u9593\u306e\u8ddd\u96e2\u300a\u7df4\u7fd2\u554f\u984c\u300b\"<\/figure>\n<\/div>\n\n\n

2\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u3092\u7528\u3044\u3066\u7df4\u7fd2\u554f\u984c\u306b\u30c1\u30e3\u30ec\u30f3\u30b8\u3057\u3066\u307f\u3088\u3046\uff01<\/p>\n\n\n\n

\u7df4\u7fd2\u554f\u984c<\/span><\/div>
\n

\u6b21\u306e2\u70b9\u9593\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u3066\u307f\u3088\u3046\u3002<\/p>\n\n\n\n

(1)\u3000\\(A\\left(1,2\\right),B\\left(4,6\\right)\\)<\/p>\n\n\n\n

(2)\u3000\\(A\\left(-3,1\\right),B\\left(2,-4\\right)\\)<\/p>\n\n\n\n

(3)\u3000\u539f\u70b9\\(O\\),\\(A\\left(2,3\\right)\\)<\/p>\n<\/div><\/div>\n\n\n

\"\"\u30b7\u30fc\u30bf<\/span><\/div>
\n

\u516c\u5f0f\u306b\u4ee3\u5165\u3059\u308b\u3060\u3051\u306a\u306e\u3067\u96e3\u3057\u304f\u306a\u3044\u306d\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

\u7df4\u7fd2\u554f\u984c(1)\u306e\u89e3\u8aac<\/h3>\n\n\n\n

2\u70b9\\(A\\left(1,2\\right),B\\left(4,6\\right)\\)\u306e\u5ea7\u6a19\u304c\u5206\u304b\u3063\u3066\u3044\u308b\u306e\u3067\u30012\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u306b\u4ee3\u5165\u3057\u3066<\/p>\n\n\n\n

\\begin{eqnarray}
AB&=&\\sqrt{\\left(4-1\\right)^{2}+\\left(6-2\\right)^{2}}\\\\
&=&\\sqrt{9+16}\\\\
&=&\\sqrt{25}\\\\
&=&5
\\end{eqnarray}<\/p>\n\n\n\n

\u3057\u305f\u304c\u3063\u3066\u30012\u70b9\\(AB\\)\u306e\u8ddd\u96e2\u306f5\u3060\u3068\u5206\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n\n

\u7df4\u7fd2\u554f\u984c(2)\u306e\u89e3\u8aac<\/h3>\n\n\n\n

\u7df4\u7fd2\u554f\u984c(2)\u3082(1)\u3068\u540c\u69d8\u306b<\/p>\n\n\n\n

\\begin{eqnarray}
AB&=&\\sqrt{\\left(2-(-3)\\right)^{2}+\\left(-4-1\\right)^{2}}\\\\
&=&\\sqrt{25+25}\\\\
&=&\\sqrt{50}\\\\
&=&5\\sqrt{2}
\\end{eqnarray}<\/p>\n\n\n\n

\u3057\u305f\u304c\u3063\u3066\u30012\u70b9\\(AB\\)\u306e\u8ddd\u96e2\u306f\\(5\\sqrt{5}\\)<\/p>\n\n\n\n

\u7df4\u7fd2\u554f\u984c(3)\u306e\u89e3\u8aac<\/h3>\n\n\n\n

\u539f\u70b9\\(O\\)\u3068\\(A\\left(2,3\\right)\\)\u306e\u8ddd\u96e2\u306a\u306e\u3067\u3001<\/p>\n\n\n\n

\\begin{eqnarray}
OA&=&\\sqrt{2^{2}+3^{2}}\\\\
&=&\\sqrt{13}
\\end{eqnarray}<\/p>\n\n\n\n

\u3057\u305f\u304c\u3063\u3066\u3001<\/p>\n\n\n\n

\\[OA=\\sqrt{13}\\]<\/p>\n\n\n

\"\"\u9ad8\u6821\u751f<\/span><\/div>
\n

\u81ea\u5206\u306e\u529b\u3067\u89e3\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\uff01<\/p>\n<\/span><\/span><\/span><\/div><\/div><\/div><\/div>\n\n\n

2\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u3000\u307e\u3068\u3081<\/h2>\n\n\n\n

\u4eca\u56de\u306f2\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/span><\/p>\n\n\n\n

2\u70b9\u9593\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u308b\u516c\u5f0f\u304c\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n

\n
\"2\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f\u306e\u8a3c\u660e\"<\/figure>\n<\/div>\n\n\n
2\u70b9\u9593\u306e\u8ddd\u96e2\u306e\u516c\u5f0f<\/span><\/div>
\n

2\u70b9\\(A\\left(x_{1},y_{1}\\right)\\),\\(B\\left(x_{2},y_{2}\\right)\\)\u9593\u306e\u8ddd\u96e2\\(AB\\)\u306f<\/p>\n\n\n\n

\\[AB=\\sqrt{\\left(x_{2}-x_{1}\\right)^{2}+\\left(y_{2}-y_{1}\\right)^{2}}\\]<\/p>\n<\/div><\/div>\n\n\n\n

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