{"id":1504,"date":"2020-07-20T23:37:58","date_gmt":"2020-07-20T15:37:58","guid":{"rendered":"https:\/\/www.study-together.com\/edu\/?page_id=1504"},"modified":"2024-04-08T17:36:15","modified_gmt":"2024-04-08T09:36:15","slug":"coordinate-geometry","status":"publish","type":"page","link":"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/coordinate-geometry\/","title":{"rendered":"8. \u5750\u6a19\u5e7e\u4f55 (Coordinate Geometry)"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-page\" data-elementor-id=\"1504\" class=\"elementor elementor-1504\">\n\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-9e7a76a elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"9e7a76a\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-66 elementor-top-column elementor-element elementor-element-1af1332\" data-id=\"1af1332\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-db18b75 elementor-widget elementor-widget-text-editor\" data-id=\"db18b75\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>8.1\u00a0 \u5750\u6a19\u5e7e\u4f55 &#8211; \u57fa\u790e\u77e5\u8b58<\/h2><p>\u672a\u958b\u59cb\u91cd\u6eab\u4e2d\u4e09\u6559\u5605\u5750\u6a19\u5e7e\u4f55\uff0c\u5efa\u8b70\u5927\u5bb6\u5148\u6eab\u7fd2\u4e00\u5413\u4e2d\u4e00\u7684\u201c<a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form1_maths\/introduction-to-coordinates\/\">\u5750\u6a19\u7c21\u4ecb<\/a>\u201d\u3002<\/p><p><img fetchpriority=\"high\" decoding=\"async\" class=\"alignright wp-image-1589 size-full\" src=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_coordinate.jpg\" alt=\"\u76f4\u89d2\u5750\u6a19\" width=\"379\" height=\"319\" srcset=\"https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_coordinate.jpg 379w, https:\/\/www.study-together.com\/edu\/wp-content\/uploads\/2020\/07\/f3maths_coordinate-300x253.jpg 300w\" sizes=\"(max-width: 379px) 100vw, 379px\" \/>\u6b64\u5916\uff0c\u55ba\u4f9d\u8ab2\u5165\u9762\uff0c\u6211\u54cb\u6703\u5229\u7528\u53f3\u908a\u5e45\u5716\u3002<\/p><p>\u7559\u610f\u5716\u4e2d\u6709\u5169\u9edeA\u3001B\uff0c\u5750\u6a19\u5206\u5225\u4fc2\\((x_{1}, y_{1})\\)\u540c\\((x_{2}, y_{2})\\)\u3002<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-121efbf elementor-widget elementor-widget-text-editor\" data-id=\"121efbf\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>8.2\u00a0 \u5169\u9ede\u9593\u7684\u8ddd\u96e2<\/h2><p>A\u3001B\u5169\u9ede\u4e4b\u9593\u7684\u8ddd\u96e2 (\u6216AB\u7dda\u6bb5\u7684\u9577\u5ea6)\u53ef\u4ee5\u4ee5\u4e0b\u516c\u5f0f\u8a08\u7b97\u51fa\u4f86\u3002<\/p><p>\\(\\quad AB = \\sqrt{(x_{2} &#8211; x_{1})^{2} + (y_{2} &#8211; y_{1})^{2}} \\)<\/p><p>\u5982\u679c\u5927\u5bb6\u6015\u8a18\u5514\u5230\u6216\u5514\u660e\u767d\u689d\u516c\u5f0f\uff0c\u53ef\u4ee5\u53c3\u5413\u4e0b\u9762\u5605\u89e3\u91cb\uff1a<\/p><ul><li style=\"list-style-type: none;\"><ul><li>AS = x<sub>2<\/sub> \u2013 x<sub>1<\/sub>\u00a0<\/li><li>BS = y<sub>2<\/sub> \u2013 y<sub>1<\/sub><\/li><li>AB\u4fc2\u76f4\u89d2\u4e09\u89d2\u5f62ABC\u7684\u659c\u908a\u3002\u53ef\u7528\u7562\u6c0f\u5b9a\u7406\u569f\u8a08\uff08\u5373\u7528\u516c\u5f0f\\(a^{2} + b^{2} = c^{2}\\)\uff09\u3002<\/li><\/ul><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-93ebf15 elementor-widget elementor-widget-text-editor\" data-id=\"93ebf15\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>8.3\u00a0 \u76f4\u7dda\u7684\u659c\u7387 (Slope of a straight line)<\/h2><p>\u76f4\u7dda\u5605\u659c\u7387\u5373\u4fc2\u4ee3\u8868\u5497\u689d\u908a\u6709\u5e7e\u659c\u540c\u659c\u5411\u908a\u4e00\u908a\u3002<\/p><p>\u6211\u54cb\u901a\u5e38\u7528\u7d30\u6977\u201cm\u201d\u4ee3\u8868\u659c\u7387\uff0c\u6240\u4ee5AB\u7684\u659c\u7387\u901a\u5e38\u6703\u5beb\u6210\u00a0 \\(m_{AB}\\)\uff08\u7559\u610fAB\u4fc2\u7d30D\u5481\u5beb\u55bam\u5605\u53f3\u4e0b\u89d2\uff09\u3002<\/p><p>\\( \\quad AB\u7684\u659c\u7387 = \\dfrac{y_{2} &#8211; y_{1}}{x_{2} &#8211; x_{1}} \\)<\/p><p>\u7559\u610f\u4e00\u5413\u6c34\u5e73\u7dda\u540c\u925b\u5782\u7dda\u5605\u659c\u7387<\/p><ul><li>\u6c34\u5e73\u7dda\uff08\u5373\u8207x-\u8ef8\u5e73\u884c\u7684\u7dda\uff09\u7684\u659c\u7387\u662f0\u3002<ul><li>\u5481\u4fc2\u56e0\u70ba\u55ba\u6c34\u5e73\u7dda\u4e0a\uff0cAB\u5169\u9ede\u5605y\u5750\u6a19\u6703\u4e00\u6a23\uff0c\u6240\u4ee5m\u6703\u7b49\u65bc0\u3002<\/li><\/ul><\/li><li>\u925b\u5782\u7dda\uff08\u5373\u8207y-\u8ef8\u5e73\u884c\u7684\u7dda\uff09\u7684\u659c\u7387\u662f\u6c92\u6709\u610f\u7fa9\u7684\u3002<ul><li>\u5481\u4fc2\u56e0\u70ba\u55ba\u925b\u5782\u7dda\u4e0a\uff0cAB\u5169\u9ede\u5605x\u5750\u6a19\u6703\u4e00\u6a23\uff0c\u6240\u4ee5m\u6703\u7b49\u65bc\u300c\\(\\dfrac{y_{2} &#8211; y_{1}}{0} \\)\u300d,\u4e00\u500b\u6578\u4fc2\u5514\u53ef\u4ee5\u88ab\u96f6\u9664\u7684\u3002<\/li><\/ul><\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-8288cc2 elementor-widget elementor-widget-text-editor\" data-id=\"8288cc2\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>8.4\u00a0 \u5e73\u884c\u7dda\u8207\u5782\u76f4\u7dda (Parallel lines and Perpendicular lines)<\/h2><ul><li>\u82e5\u5169\u689d\u7dda\u4e92\u76f8\u5e73\u884c\uff0c\u5247\u5b83\u5011\u7684\u659c\u7387\u76f8\u7b49\uff0c\u5373 m<sub>1<\/sub> = m<sub>2<\/sub><\/li><li>\u82e5\u5169\u689d\u7dda\u4e92\u76f8\u5782\u76f4\uff0c\u5247 m<sub>1<\/sub> x m<sub>2<\/sub> = &#8211; 1<\/li><\/ul>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-2de86d1 elementor-widget elementor-widget-text-editor\" data-id=\"2de86d1\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>8.5\u00a0 \u5206\u9ede\u5169\u9ede\u7684\u4e2d\u9ede (Mid-point of 2 points)<\/h2><p>\u82e5M\u9ede\u662fAB\u7dda\u6bb5\u4e0a\u7684\u4e2d\u9593\u9ede\uff0c\u5247M\u7684\u5750\u6a19(x, y) \u53ef\u7528\u4ee5\u4e0b\u516c\u5f0f\u8a08\u7b97\u51fa\u4f86\u3002<\/p><p>\\(\\quad x = \\dfrac{x_{1} + x_{2}}{2} \\quad\uff0cx = \\dfrac{y_{1} + y_{2}}{2} \\)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-524b302 elementor-widget elementor-widget-text-editor\" data-id=\"524b302\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<h2>8.6\u00a0 \u5206\u9ede (Point of Division)<\/h2><p>\u82e5P\u9ede\u662fAB\u7dda\u6bb5\u4e0a\u7684\u4e00\u9ede\u4f7f\u3000AP : PB = r : s\uff0c\u5247P\u9ede\u7684\u5750\u6a19(x, y)\u70ba\uff1a<\/p><p>\\(\\quad x = \\dfrac{sx_{1} + rx_{2}}{r + s} \\quad\uff0cx = \\dfrac{sy_{1} + ry_{2}}{r + s} \\)<\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<section class=\"elementor-section elementor-inner-section elementor-element elementor-element-86cdf5c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"86cdf5c\" data-element_type=\"section\" data-e-type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-a800596\" data-id=\"a800596\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-09c24c6 elementor-widget elementor-widget-text-editor\" data-id=\"09c24c6\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/area-volume\/\"><i class=\"far fa-arrow-alt-circle-left\" aria-hidden=\"true\"><\/i> \u9762\u7a4d\u8207\u9ad4\u7a4d<\/a>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-1bde3be\" data-id=\"1bde3be\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap\">\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-inner-column elementor-element elementor-element-22ab8ec\" data-id=\"22ab8ec\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-d7019ed elementor-widget elementor-widget-text-editor\" data-id=\"d7019ed\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t\t\t<p style=\"text-align: right;\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/trigonometry\/\">\u4e09\u89d2\u6bd4 <i class=\"far fa-arrow-alt-circle-right\" aria-hidden=\"true\"><\/i><\/a><\/p>\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t<div class=\"elementor-column elementor-col-33 elementor-top-column elementor-element elementor-element-fba9a9d\" data-id=\"fba9a9d\" data-element_type=\"column\" data-e-type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e3e7f46 elementor-widget elementor-widget-sidebar\" data-id=\"e3e7f46\" data-element_type=\"widget\" data-e-type=\"widget\" data-widget_type=\"sidebar.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"sidebar-box widget-oceanwp-custom-menu custom-menu-widget clr\"><style type=\"text\/css\">.ocean_custom_menu-4 > ul > li > a, .custom-menu-widget .ocean_custom_menu-4 .dropdown-menu .sub-menu li a.menu-link{font-size:16px;line-height:17px;}.custom-menu-widget .ocean_custom_menu-4.oceanwp-custom-menu > ul.click-menu .open-this{font-size:16px;}<\/style><h4 class=\"widget-title\">\u4e2d\u4e09\u6578\u5b78\u3010\u76ee\u9304\u3011<\/h4><div class=\"oceanwp-custom-menu clr ocean_custom_menu-4 left dropdown-hover\"><ul id=\"menu-form3mathstopics\" class=\"dropdown-menu sf-menu\"><li  id=\"menu-item-1543\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1543\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/inequalities\/\" class=\"menu-link\">1. \u4e0d\u7b49\u5f0f (Inequalities)<\/a><\/li>\n<li  id=\"menu-item-1542\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1542\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/indices\/\" class=\"menu-link\">2. \u6307\u6578 (Indices)<\/a><\/li>\n<li  id=\"menu-item-1541\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1541\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/use-of-percentage\/\" class=\"menu-link\">3. \u767e\u4efd\u6cd5  (Use of Percentage)<\/a><\/li>\n<li  id=\"menu-item-1540\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1540\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/rational-irrational-numbers\/\" class=\"menu-link\">4. \u6709\u7406\u6578\u53ca\u7121\u7406\u6578 (Rational &#038; Irrational Numbers)<\/a><\/li>\n<li  id=\"menu-item-1539\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1539\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/deductive-geometry\/\" class=\"menu-link\">5. \u6f14\u7e79\u5e7e\u4f55 (Deductive Geometry)<\/a><\/li>\n<li  id=\"menu-item-1538\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1538\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/quadrilateral\/\" class=\"menu-link\">6. \u56db\u908a\u5f62 (Quadrilateral)<\/a><\/li>\n<li  id=\"menu-item-1537\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1537\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/area-volume\/\" class=\"menu-link\">7. \u9762\u7a4d\u8207\u9ad4\u7a4d (Area &#038; Volume)<\/a><\/li>\n<li  id=\"menu-item-1536\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1536\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/coordinate-geometry\/\" class=\"menu-link\">8. \u5750\u6a19\u5e7e\u4f55 (Coordinate Geometry)<\/a><\/li>\n<li  id=\"menu-item-1535\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1535\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/trigonometry\/\" class=\"menu-link\">9. \u4e09\u89d2\u5b78 (Trigonometry)<\/a><\/li>\n<li  id=\"menu-item-1534\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1534\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/applications-of-trigonometry\/\" class=\"menu-link\">10. \u4e09\u89d2\u6bd4\u7684\u61c9\u7528 (Applications of Trigonometry)<\/a><\/li>\n<li  id=\"menu-item-1533\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1533\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/probability\/\" class=\"menu-link\">11. \u6982\u7387 (Probability)<\/a><\/li>\n<li  id=\"menu-item-1532\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1532\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/statistics-measure-of-central-tendency\/\" class=\"menu-link\">12. \u7d71\u8a08 \u2013 \u96c6\u4e2d\u8da8\u52e2\u7684\u91cf\u5ea6 (Measure of Central Tendency)<\/a><\/li>\n<li  id=\"menu-item-1625\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-1625\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/form3_maths\/centers-of-triangles\/\" class=\"menu-link\">13. \u4e09\u89d2\u5f62\u7684\u5fc3 (Centers of Triangles)<\/a><\/li>\n<li  id=\"menu-item-16136\" class=\"menu-item menu-item-type-post_type menu-item-object-page menu-item-16136\"><a href=\"https:\/\/www.study-together.com\/edu\/secondary\/exam_papers\/\" class=\"menu-link\">*** \u521d\u4e2d\u8a66\u5377 \/ \u8a66\u984c\u5eab ***<\/a><\/li>\n<\/ul><\/div><\/div>\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>8.1\u00a0 \u5750\u6a19\u5e7e\u4f55 &#8211; \u57fa\u790e\u77e5\u8b58 \u672a\u958b\u59cb\u91cd\u6eab\u4e2d\u4e09\u6559\u5605\u5750\u6a19\u5e7e\u4f55\uff0c\u5efa\u8b70\u5927\u5bb6\u5148\u6eab\u7fd2\u4e00\u5413\u4e2d\u4e00\u7684\u201c\u5750\u6a19\u7c21\u4ecb\u201d 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