{"id":11144,"date":"2022-11-21T13:45:28","date_gmt":"2022-11-21T04:45:28","guid":{"rendered":"https:\/\/hatsudy.com\/jp\/?p=11144"},"modified":"2022-11-25T15:56:29","modified_gmt":"2022-11-25T06:56:29","slug":"point","status":"publish","type":"post","link":"https:\/\/hatsudy.com\/jp\/point.html","title":{"rendered":"\u76f4\u7dda\u4e0a\u30fb\u5e73\u9762\u4e0a\u306e\u70b9\uff1a\u5185\u5206\u70b9\u3001\u5916\u5206\u70b9\u3001\u91cd\u5fc3\u3001\u5bfe\u79f0\u306e\u70b9"},"content":{"rendered":"\n<p>\u6570\u5b66\u3067\u76f4\u7dda\u4e0a\u306e\u70b9\u3092\u8003\u3048\u308b\u3068\u304d\u3001\u6700\u3082\u91cd\u8981\u306a\u8981\u7d20\u304c\u8ddd\u96e2\u3067\u3059\u30022\u3064\u306e\u70b9\u3092\u5229\u7528\u3059\u308c\u3070\u3001\u7dda\u5206\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u307e\u305f\u3001\u8ddd\u96e2\u4ee5\u5916\u306b\u91cd\u8981\u306a\u6982\u5ff5\u304c\u5185\u5206\u70b9\u3068\u5916\u5206\u70b9\u3067\u3059\u3002\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u5185\u5206\u70b9\u3068\u5916\u5206\u70b9\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u306a\u304a\u70b9\u306f\u76f4\u7dda\u4e0a\u3067\u306f\u306a\u304f\u3001\u5e73\u9762\u4e0a\u306b\u5b58\u5728\u3059\u308b\u3053\u3068\u3082\u591a\u3044\u3067\u3059\u3002\u305d\u3053\u3067\u3001\u5e73\u9762\u4e0a\u30672\u70b9\u9593\u306e\u8ddd\u96e2\u3092\u51fa\u305b\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u4e09\u5e73\u65b9\u306e\u5b9a\u7406\u3092\u5229\u7528\u3059\u308c\u3070\u30012\u70b9\u9593\u306e\u8ddd\u96e2\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u307e\u305f\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u5185\u5206\u70b9\u3068\u5916\u5206\u70b9\u3092\u51fa\u3059\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u306b\u52a0\u3048\u3066\u3001\u4e09\u89d2\u5f62\u306e\u91cd\u5fc3\u3084\u5bfe\u79f0\u306a\u70b9\u3092\u5f97\u3089\u308c\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u91cd\u5fc3\u306e\u8a08\u7b97\u3067\u306f\u516c\u5f0f\u3092\u5229\u7528\u3057\u307e\u3059\u3002\u5bfe\u79f0\u306a\u70b9\u3067\u306f\u30012\u3064\u306e\u70b9\u3092\u8db3\u3057\u30662\u3067\u5272\u308c\u3070\u5bfe\u79f0\u306a\u70b9\u306e\u5ea7\u6a19\u3092\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\u76f4\u7dda\u4e0a\u306e\u70b9\u3068\u5e73\u9762\u4e0a\u306e\u70b9\u306b\u3064\u3044\u3066\u3001\u660e\u78ba\u306a\u5ea7\u6a19\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u3069\u306e\u3088\u3046\u306b\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u304b\u89e3\u8aac\u3057\u3066\u3044\u304d\u307e\u3059\u3002<\/p>\n<h2>\u76f4\u7dda\u4e0a\u306e\u7dda\u5206\u306e\u5185\u5206\u70b9\u3068\u5916\u5206\u70b9\uff1a\u5ea7\u6a19\u3068\u516c\u5f0f<\/h2>\n<p>\u7dda\u5206\u306e\u9577\u3055\u3092\u8a08\u7b97\u3059\u308b\u306e\u306f\u5bb9\u6613\u3067\u3059\u3002\u70b9\\(a\\)\u3068\u70b9\\(b\\)\u306e\u8ddd\u96e2\u306f\\(|b-a|\\)\u3067\u3059\u3002\u70b9\\(a\\)\u3068\u70b9\\(b\\)\u306b\u3064\u3044\u3066\u3001\u3069\u3061\u3089\u306e\u5024\u304c\u5927\u304d\u3044\u306e\u304b\u308f\u304b\u308a\u307e\u305b\u3093\u3002\u305d\u3053\u3067\u3001\u7d76\u5bfe\u5024\u3092\u52a0\u3048\u308b\u3053\u3068\u3067\u5fc5\u305a\u6b63\u306e\u5024\u306b\u5909\u63db\u3057\u307e\u3059\u3002<\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u5185\u5206\u70b9\u306f\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u7dda\u5206\u3092\u5185\u5074\u3067\u5206\u3051\u308b\u70b9\u3092\u5185\u5206\u70b9\u3068\u3044\u3044\u307e\u3059\u3002\u4f8b\u3048\u3070\u70b9O\u304c\u539f\u70b9\u3067\u3042\u308a\u3001OA\u306e\u9577\u3055\u304c3\u306e\u3068\u304d\u3001OA\u30921:2\u306b\u5185\u5206\u3059\u308b\u70b9B\u306f\u3069\u3053\u306b\u3042\u308b\u3067\u3057\u3087\u3046\u304b\u3002\u70b9B\u304cOA\u30921:2\u306b\u5185\u5206\u3059\u308b\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/ejfh4.jpg\" alt=\"\" width=\"279\" height=\"160\" class=\"aligncenter size-full wp-image-11149\" \/><\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u70b9B\u306e\u5ea7\u6a19\u304c\u308f\u304b\u308a\u307e\u3059\u3002\\(OB:BA=1:2\\)\u3068\u306a\u3063\u3066\u3044\u307e\u3059\u3002<\/p>\n<p>\u4e00\u65b9\u3067OA\u306e\u9577\u3055\u304c3\u306e\u3068\u304d\u3001OA\u30921:2\u306b\u5916\u5206\u3059\u308b\u70b9B\u306f\u3069\u3053\u306b\u3042\u308b\u3067\u3057\u3087\u3046\u304b\u3002\u70b9B\u304cOA\u30921:2\u306b\u5916\u5206\u3059\u308b\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/ejfh8.jpg\" alt=\"\" width=\"545\" height=\"166\" class=\"aligncenter size-full wp-image-11153\" \/><\/p>\n<p>\u3053\u306e\u5834\u5408\u3067\u3042\u3063\u3066\u3082\u3001\\(OB:BA=1:2\\)\u3067\u3059\u3002\u305f\u3060\u5148\u307b\u3069\u3068\u306f\u7570\u306a\u308a\u3001\u70b9B\u306f\u7dda\u5206OA\u306e\u5916\u5074\u306b\u3042\u308a\u307e\u3059\u3002\u3053\u3046\u3057\u305f\u70b9\u304c\u5916\u5206\u70b9\u3067\u3059\u3002<\/p>\n<p><strong>\u30fb\u5185\u5206\u70b9\u3068\u5916\u5206\u70b9\u306e\u516c\u5f0f<\/strong><\/p>\n<p>\u306a\u304a\u5b9f\u969b\u306b\u306f\u3001\u539f\u70b9O\u3092\u5229\u7528\u305b\u305a\u30012\u3064\u306e\u70b9\uff08\u70b9A\u3068\u70b9B\uff09\u3092\u5185\u5206\u3059\u308b\u70b9\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u591a\u3044\u3067\u3059\u3002\u70b9A\u306e\u5ea7\u6a19\u3092\\(a\\)\u3001\u70b9B\u306e\u5ea7\u6a19\u3092\\(b\\)\u3001\u7dda\u5206AB\u306e\u5185\u5206\u70b9\u3092\u70b9P\uff08\u5ea7\u6a19\\(x\\)\uff09\u3068\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u56f3\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/ejfh6.jpg\" alt=\"\" width=\"283\" height=\"99\" class=\"aligncenter size-full wp-image-11151\" \/><\/p>\n<p>\u70b9P\u304c\u7dda\u5206AB\u3092\\(m:n\\)\u306b\u5185\u5206\u3059\u308b\u5834\u5408\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(AP:PB=x-a:b-x=m:n\\)<\/p>\n<p>\\(n(x-a)=m(b-x)\\)<\/p>\n<p>\\(x(n+m)=na+mb\\)<\/p>\n<p>\\(x=\\displaystyle\\frac{na+mb}{m+n}\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u7dda\u5206\u3092\u5185\u5206\u3059\u308b\u516c\u5f0f\u3092\u5f97\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3057\u305f\u3002\u306a\u304a\u3001\u7dda\u5206AB\u3092\\(m:n\\)\u306b\u5916\u5206\u3059\u308b\u70b9P\u3092\u5f97\u308b\u516c\u5f0f\u306f\u4ee5\u4e0b\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x=\\displaystyle\\frac{-na+mb}{m-n}\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/ejfh9.jpg\" alt=\"\" width=\"531\" height=\"97\" class=\"aligncenter size-full wp-image-11154\" \/><\/p>\n<p><span style=\"color: #0000ff;\">\u5916\u5206\u70b9P\u306e\u5ea7\u6a19\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\\(m:(-n)\\)\u306b\u5185\u5206\u3059\u308b\u3068\u8003\u3048\u307e\u3057\u3087\u3046\u3002<\/span>\u305d\u306e\u305f\u3081\u5185\u5206\u70b9\u3092\u5f97\u308b\u516c\u5f0f\u3092\u5909\u5f62\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u5916\u5206\u70b9\u3092\u5f97\u308b\u516c\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<h3>\u5e73\u9762\u4e0a\u306e\u7dda\u5206\u306e\u5185\u5206\u70b9\u3068\u5916\u5206\u70b9<\/h3>\n<p>\u306a\u304a\u5185\u5206\u70b9\u3068\u5916\u5206\u70b9\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u76f4\u7dda\u4e0a\u306b\u70b9\u304c\u5b58\u5728\u3059\u308b\u306e\u3067\u306f\u306a\u304f\u3001\u5e73\u9762\u4e0a\u306b\u70b9\u304c\u5b58\u5728\u3059\u308b\u30b1\u30fc\u30b9\u304c\u3072\u3093\u3071\u3093\u306b\u3042\u308a\u307e\u3059\u3002\u305d\u306e\u5834\u5408\u3001\\(x\\)\u8ef8\u3068\\(y\\)\u8ef8\u306b\u5206\u3051\u3066\u5185\u5206\u70b9\uff08\u307e\u305f\u306f\u5916\u5206\u70b9\uff09\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u4f8b\u3048\u3070\u3001\u70b9A\\((x_a,y_a)\\)\u3068\u70b9B\\((x_b,y_b)\\)\u3092\\(m:n\\)\u306b\u5185\u5206\u3059\u308b\u70b9P\u306e\u5ea7\u6a19\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x\\)\u5ea7\u6a19\uff1a\\(\\displaystyle\\frac{nx_a+mx_b}{m+n}\\)<\/li>\n<li>\\(y\\)\u5ea7\u6a19\uff1a\\(\\displaystyle\\frac{ny_a+my_b}{m+n}\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/ejfh13.jpg\" alt=\"\" width=\"438\" height=\"337\" class=\"aligncenter size-full wp-image-11160\" \/><\/p>\n<p>\u307e\u305f\u3001\u5916\u5206\u70b9P\u306e\u5ea7\u6a19\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x\\)\u5ea7\u6a19\uff1a\\(\\displaystyle\\frac{-nx_a+mx_b}{m-n}\\)<\/li>\n<li>\\(y\\)\u5ea7\u6a19\uff1a\\(\\displaystyle\\frac{-ny_a+my_b}{m-n}\\)<\/li>\n<\/ul>\n<p>\\(x\\)\u8ef8\u3068\\(y\\)\u8ef8\u3092\u305d\u308c\u305e\u308c\u5206\u3051\u3066\u8a08\u7b97\u3059\u308b\u3053\u3068\u3092\u7406\u89e3\u3059\u308c\u3070\u3001\u5e73\u9762\u4e0a\u306e\u7dda\u5206\u306b\u5bfe\u3059\u308b\u5185\u5206\u70b9\u3068\u5916\u5206\u70b9\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<h3>\u5e73\u9762\u4e0a\u306e2\u70b9\u9593\u306e\u8ddd\u96e2<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u5e73\u9762\u4e0a\u306e2\u70b9\u9593\u306e\u8ddd\u96e2\u306f\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u8a08\u7b97\u65b9\u6cd5\u306f\u7c21\u5358\u3067\u3042\u308a\u3001\u4e09\u5e73\u65b9\u306e\u5b9a\u7406\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u5e73\u9762\u4e0a\u306e\u70b9A\\((x_a,y_a)\\)\u3068\u70b9B\\((x_b,y_b)\\)\u306b\u3064\u3044\u3066\u3001\u8ddd\u96e2\u3092\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002\u4e09\u5e73\u65b9\u306e\u5b9a\u7406\u3092\u5229\u7528\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(AB=\\sqrt{(x_b-x_a)^2+(y_b-y_a)^2}\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/doepl1.jpg\" alt=\"\" width=\"533\" height=\"331\" class=\"aligncenter size-full wp-image-11173\" \/><\/p>\n<p>\u65e2\u306b\u77e5\u3063\u3066\u3044\u308b\u4e8b\u5b9f\u3067\u3042\u308b\u305f\u3081\u3001\u3053\u306e\u516c\u5f0f\u306f\u4f55\u3082\u554f\u984c\u306a\u304f\u7406\u89e3\u3067\u304d\u308b\u3068\u601d\u3044\u307e\u3059\u3002\u305d\u308c\u3067\u306f\u3001\u4ee5\u4e0b\u306e\u554f\u984c\u306e\u7b54\u3048\u306f\u4f55\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<ul>\n<li>\u70b9A\\((1,2)\\)\u3068\u70b9B\\((4,-1)\\)\u304b\u3089\u7b49\u8ddd\u96e2\u306b\u3042\u308b\\(x\\)\u8ef8\u4e0a\u306e\u70b9P\u306e\u5ea7\u6a19\u3092\u6c42\u3081\u307e\u3057\u3087\u3046\u3002<\/li>\n<\/ul>\n<p>\\(x\\)\u8ef8\u4e0a\u306e\u70b9P\u306e\u5ea7\u6a19\u3092\\((x,0)\\)\u3068\u3057\u307e\u3057\u3087\u3046\u3002\\(AP=BP\\)\u306a\u306e\u3067\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(AP^2=BP^2\\)<\/p>\n<p>\\((1-x)^2+2^2=(4-x)^2+(-1)^2\\)<\/p>\n<p>\\(x^2-2x+5=x^2-8x+17\\)<\/p>\n<p>\\(6x=12\\)<\/p>\n<p>\\(x=2\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u70b9P\u306e\u5ea7\u6a19\u306f\\((2,0)\\)\u3068\u308f\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n<h2>\u4e09\u89d2\u5f62\u306e\u91cd\u5fc3\u3068\u516c\u5f0f<\/h2>\n<p>\u5e73\u9762\u4e0a\u306e\u70b9\u3067\u307b\u304b\u306b\u91cd\u8981\u306a\u516c\u5f0f\u3068\u3057\u3066\u3001\u4e09\u89d2\u5f62\u306e\u91cd\u5fc3\u3092\u6c42\u3081\u308b\u516c\u5f0f\u304c\u3042\u308a\u307e\u3059\u3002\u4ee5\u4e0b\u306e\u25b3ABC\u306b\u3064\u3044\u3066\u30013\u8fbaAB\u3001BC\u3001CA\u306e\u4e2d\u70b9\u3068\u305d\u308c\u305e\u308c\u306e\u9802\u70b9\u3092\u7d50\u3076\u5834\u5408\u3001\u4ea4\u308f\u308b\u70b9G\u3092\u91cd\u5fc3\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/ejfh15.jpg\" alt=\"\" width=\"435\" height=\"318\" class=\"aligncenter size-full wp-image-11162\" \/><\/p>\n<p><span style=\"color: #0000ff;\">\u91cd\u5fc3G\u306f\u300c\u9802\u70b9\u3068\u4e2d\u70b9\u3092\u7d50\u3076\u7dda\u30922:1\u3067\u5185\u5206\u3059\u308b\u70b9\u300d\u3067\u3059\u3002<\/span><\/p>\n<p>\u305d\u308c\u3067\u306f\u3001\u91cd\u5fc3G\u306e\u5ea7\u6a19\u306f\u3069\u306e\u3088\u3046\u306b\u8a08\u7b97\u3059\u308c\u3070\u3044\u3044\u306e\u3067\u3057\u3087\u3046\u304b\u3002\u9802\u70b9\u306e\u5ea7\u6a19\u3092A\\((x_a,y_a)\\)\u3001B\\((x_b,y_b)\\)\u3001C\\((x_c,y_c)\\)\u3068\u3059\u308b\u3068\u3001\u91cd\u5fc3G\u306e\u5ea7\u6a19\u306f\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(x\\)\u5ea7\u6a19\uff1a\\(\\displaystyle\\frac{x_a+x_b+x_c}{3}\\)<\/li>\n<li>\\(y\\)\u5ea7\u6a19\uff1a\\(\\displaystyle\\frac{y_a+y_b+y_c}{3}\\)<\/li>\n<\/ul>\n<p>\u4e09\u89d2\u5f62\u306e\u91cd\u5fc3\u3092\u5f97\u308b\u516c\u5f0f\u306f\u899a\u3048\u3066\u3057\u307e\u3044\u307e\u3057\u3087\u3046\u3002<\/p>\n<h3>\u5ea7\u6a19\u3092\u5229\u7528\u3057\u3066\u8a3c\u660e\u3059\u308b<\/h3>\n<p>\u305d\u308c\u3067\u306f\u3001\u5ea7\u6a19\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u8a3c\u660e\u554f\u984c\u3092\u89e3\u3044\u3066\u307f\u307e\u3057\u3087\u3046\u3002\u25b3ABC\u306e\u91cd\u5fc3\u3092G\u3068\u3059\u308b\u3068\u304d\u3001\u4ee5\u4e0b\u304c\u6210\u308a\u7acb\u3064\u3053\u3068\u3092\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<ul>\n<li>\\(AB^2+BC^2+CA^2\\)\\(=3(GA^2+GB^2+GC^2)\\)<\/li>\n<\/ul>\n<p>\u5ea7\u6a19\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u3067\u8a3c\u660e\u3057\u307e\u3057\u3087\u3046\u3002\u3069\u306e\u5834\u6240\u3092\u539f\u70b9O\u306b\u8a2d\u5b9a\u3057\u3066\u3082\u3044\u3044\u3067\u3059\u304c\u3001\u8a08\u7b97\u3092\u697d\u306b\u3059\u308b\u305f\u3081\u3001\\(x\\)\u8ef8\u3068\\(y\\)\u8ef8\u30670\u3068\u306a\u308b\u7b87\u6240\u304c\u591a\u304f\u306a\u308b\u3088\u3046\u306b\u539f\u70b9O\u3092\u8a2d\u5b9a\u3057\u307e\u3057\u3087\u3046\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306bAB\u306e\u4e2d\u70b9\u3092\u539f\u70b9O\u306b\u3057\u307e\u3059\u3002<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/ejfh16.jpg\" alt=\"\" width=\"467\" height=\"328\" class=\"aligncenter size-full wp-image-11163\" \/><\/p>\n<p>\u3053\u3053\u307e\u3067\u89e3\u8aac\u3057\u305f\u5185\u5bb9\u3092\u5229\u7528\u3059\u308b\u3068\u3001\u305d\u308c\u305e\u308c\u306e\u5ea7\u6a19\u3092\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8868\u3059\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<ul>\n<li>A\\((-p,0)\\)<\/li>\n<li>B\\((p,0)\\)<\/li>\n<li>C\\((3q,3r)\\)<\/li>\n<li>G\\((q,r)\\)<\/li>\n<\/ul>\n<p>\u539f\u70b9O\u306fAB\u306e\u4e2d\u70b9\u3067\u3042\u308b\u305f\u3081\u3001\u70b9A\u306e\u5ea7\u6a19\u3092\\((-p,0)\\)\u3068\u3059\u308b\u3068\u3001\u70b9B\u306e\u5ea7\u6a19\u306f\\((p,0)\\)\u3067\u3059\u3002\u307e\u305f\u91cd\u5fc3G\u306e\u5ea7\u6a19\u3092\\((q,r)\\)\u3068\u3059\u308b\u3068\u3001\u70b9G\u306fCO\u30922:1\u306b\u5185\u5206\u3059\u308b\u305f\u3081\u3001\u70b9C\u306e\u5ea7\u6a19\u306f\\((3q,3r)\\)\u3068\u306a\u308a\u307e\u3059\u3002\u305d\u3053\u3067\u3001\u4ee5\u4e0b\u306e\u3088\u3046\u306b\u8a08\u7b97\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(AB^2+BC^2+CA^2\\)<\/p>\n<p>\\(=4p^2+(3q-p)^2+9r^2+(3q+p)^2\\)\\(+9r^2\\)<\/p>\n<p>\\(=4p^2+(9q^2-6qp+p^2)\\)\\(+(9q^2+6qp+p^2)\\)\\(+18r^2\\)<\/p>\n<p>\\(=6p^2+18q^2+18r^2\\)<\/p>\n<p>\u6b21\u306b\u3001\u4ee5\u4e0b\u306e\u8a08\u7b97\u3092\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\\(3(GA^2+GB^2+GC^2)\\)<\/p>\n<p>\\(=3(q+p)^2+3r^2+3(q-p)^2+3r^2\\)\\(+12q^2\\)\\(+12r^2\\)<\/p>\n<p>\\(=3(q^2+2qp+p^2)\\)\\(+3(q^2-2qp+p^2)\\)\\(+12q^2\\)\\(+18r^2\\)<\/p>\n<p>\\(=6p^2+18q^2+18r^2\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u540c\u3058\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u305f\u305f\u3081\u3001\\(AB^2+BC^2+CA^2\\)\\(=3(GA^2+GB^2+GC^2)\\)\u304c\u6210\u308a\u7acb\u3064\u3068\u8a3c\u660e\u3067\u304d\u307e\u3057\u305f\u3002<\/p>\n<h2>\u70b9\u306b\u5bfe\u3057\u3066\u5bfe\u79f0\u306a\u70b9\u306e\u6c42\u3081\u65b9<\/h2>\n<p>\u5e73\u9762\u4e0a\u306e\u70b9\u3067\u306f\u3001\u7279\u5b9a\u306e\u70b9\u306b\u5bfe\u3057\u3066\u5bfe\u79f0\u306a\u70b9\u3092\u6c42\u3081\u306a\u3051\u308c\u3070\u3044\u3051\u306a\u3044\u3053\u3068\u3082\u3042\u308a\u307e\u3059\u3002\u4f8b\u3048\u3070\u70b9A\\((1,2)\\)\u3092\u57fa\u6e96\u306b\u3059\u308b\u3068\u304d\u3001\\((4,5)\\)\u3068\u5bfe\u79f0\u306a\u70b9\u306f\u3069\u3053\u3067\u3057\u3087\u3046\u304b\u3002<\/p>\n<p>\u5bfe\u79f0\u306a\u70b9\u3092\\((x,y)\\)\u3068\u3057\u307e\u3057\u3087\u3046\u3002\u70b9A\u3092\u57fa\u6e96\u306b\u5bfe\u79f0\u3068\u3044\u3046\u306e\u306f\u3001\u70b9A\u304c\\((4,5)\\)\u3068\\((x,y)\\)\u306e\u4e2d\u70b9\u3067\u3042\u308b\u3053\u3068\u3092\u610f\u5473\u3057\u3066\u3044\u307e\u3059\u3002\u305d\u306e\u305f\u3081\\(x\\)\u8ef8\u306b\u7740\u76ee\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(1=\\displaystyle\\frac{4+x}{2}\\)<\/p>\n<p>\\(x=-2\\)<\/p>\n<p>\u307e\u305f\\(y\\)\u8ef8\u306b\u7740\u76ee\u3059\u308b\u3068\u3001\u4ee5\u4e0b\u306e\u5f0f\u3092\u4f5c\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n<p>\\(2=\\displaystyle\\frac{5+y}{2}\\)<\/p>\n<p>\\(y=-1\\)<\/p>\n<p>\u3053\u3046\u3057\u3066\u3001\u5bfe\u79f0\u306a\u70b9\u306e\u5ea7\u6a19\u306f\\((-2,-1)\\)\u3068\u308f\u304b\u308a\u307e\u3059\u3002<\/p>\n<p><span style=\"color: #0000ff;\">\u7279\u5b9a\u306e\u70b9\u306b\u5bfe\u3057\u3066\u5bfe\u79f0\u306a\u70b9\u3092\u6c42\u3081\u308b\u3068\u3044\u3046\u306e\u306f\u3001\u4e2d\u70b9\u306e\u6027\u8cea\u3092\u5229\u7528\u3057\u3066\u8a08\u7b97\u3059\u308b\u306e\u3068\u610f\u5473\u304c\u540c\u3058\u3067\u3059\u3002<\/span>\u305d\u306e\u305f\u3081\u70b9A\\((a,b)\\)\u306b\u5bfe\u3057\u3066\u30012\u70b9P\\((x_p,y_p)\\)\u3068Q\\((x_q,y_q)\\)\u304c\u5bfe\u79f0\u306e\u3068\u304d\u3001\u4ee5\u4e0b\u306e\u95a2\u4fc2\u304c\u6210\u308a\u7acb\u3061\u307e\u3059\u3002<\/p>\n<ul>\n<li>\\(a=\\displaystyle\\frac{x_p+x_q}{2}\\)<\/li>\n<li>\\(b=\\displaystyle\\frac{y_p+y_q}{2}\\)<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/hatsudy.com\/jp\/wp-content\/uploads\/2022\/11\/iwh6.jpg\" alt=\"\" width=\"493\" height=\"317\" class=\"aligncenter size-full wp-image-11229\" \/><\/p>\n<p>\u70b9\u306b\u5bfe\u3057\u3066\u5bfe\u79f0\u306a\u70b9\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u4e2d\u70b9\u306e\u6027\u8cea\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<h2>\u76f4\u7dda\u4e0a\u306e\u70b9\u3068\u5e73\u9762\u4e0a\u306e\u70b9\u3067\u306e\u5ea7\u6a19\u3092\u8a08\u7b97\u3059\u308b<\/h2>\n<p>\u7279\u5b9a\u306e\u70b9\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u3053\u3068\u306f\u91cd\u8981\u3067\u3059\u3002\u4f8b\u3048\u3070\u6e2c\u91cf\u3092\u3057\u305f\u308a\u3001\u5efa\u7269\u56f3\u5f62\u306e\u8a08\u7b97\u3092\u3057\u305f\u308a\u3059\u308b\u3068\u304d\u3001\u5ea7\u6a19\u3092\u6c42\u3081\u3089\u308c\u308b\u3088\u3046\u306b\u306a\u3089\u306a\u3051\u308c\u3070\u3044\u3051\u307e\u305b\u3093\u3002<\/p>\n<p>\u305d\u3053\u3067\u76f4\u7dda\u4e0a\u306e\u70b9\u3068\u5e73\u9762\u4e0a\u306e\u70b9\u306b\u3064\u3044\u3066\u3001\u5ea7\u6a19\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002\u7dda\u306e\u9577\u3055\u3092\u8a08\u7b97\u3057\u305f\u308a\u3001\u5185\u5206\u70b9\u30fb\u5916\u5206\u70b9\u3092\u5f97\u305f\u308a\u3059\u308b\u306e\u3067\u3059\u3002\u5185\u5206\u70b9\u3068\u5916\u5206\u70b9\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u3001\u516c\u5f0f\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u306a\u304a\u5e73\u9762\u4e0a\u306e\u70b9\u3092\u5b66\u3076\u3068\u304d\u3001\u4e09\u89d2\u5f62\u306e\u91cd\u5fc3\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a\u308b\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u9802\u70b9\u3068\u4e2d\u70b9\u3092\u7d50\u3076\u3068\u304d\u30012:1\u306b\u5185\u5206\u3059\u308b\u70b9\u304c\u91cd\u5fc3\u3067\u3059\u3002\u307e\u305f\u3001\u91cd\u5fc3\u306e\u4f4d\u7f6e\u3092\u8a08\u7b97\u3059\u308b\u3068\u304d\u306f\u516c\u5f0f\u3092\u5229\u7528\u3057\u307e\u3057\u3087\u3046\u3002<\/p>\n<p>\u56f3\u5f62\u306b\u304a\u3044\u3066\u3001\u70b9\u306e\u5ea7\u6a19\u3092\u8a08\u7b97\u3059\u308b\u306e\u306f\u6700\u3082\u57fa\u672c\u7684\u306a\u5185\u5bb9\u306e\u4e00\u3064\u3067\u3059\u3002\u305d\u3053\u3067\u516c\u5f0f\u3092\u5229\u7528\u3057\u3066\u3001\u5ea7\u6a19\u3092\u5f97\u3089\u308c\u308b\u3088\u3046\u306b\u306a\u308a\u307e\u3057\u3087\u3046\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6570\u5b66\u3067\u76f4\u7dda\u4e0a\u306e\u70b9\u3092\u8003\u3048\u308b\u3068\u304d\u3001\u6700\u3082\u91cd\u8981\u306a\u8981\u7d20\u304c\u8ddd\u96e2\u3067\u3059\u30022\u3064\u306e\u70b9\u3092\u5229\u7528\u3059\u308c\u3070\u3001\u7dda\u5206\u306e\u8ddd\u96e2\u3092\u6c42\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u307e\u305f\u3001\u8ddd\u96e2\u4ee5\u5916\u306b\u91cd\u8981\u306a\u6982\u5ff5\u304c\u5185\u5206\u70b9\u3068\u5916\u5206\u70b9\u3067\u3059\u3002\u516c\u5f0f\u3092\u5229\u7528\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u5185\u5206\u70b9\u3068\u5916\u5206\u70b9\u3092\u8a08\u7b97\u3067\u304d\u308b\u3088\u3046\u306b\u306a 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