{"id":4663,"date":"2022-08-31T19:42:28","date_gmt":"2022-08-31T17:42:28","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/analyticka-geometrie-priklad-1\/"},"modified":"2022-09-01T12:08:42","modified_gmt":"2022-09-01T10:08:42","slug":"analyticka-geometrie-priklad-1","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/analyticka-geometrie-priklad-1\/","title":{"rendered":"Analytick\u00e1 geometrie &#8211; p\u0159\u00edklad 1"},"content":{"rendered":"<p><strong> Zad\u00e1n\u00ed p\u0159\u00edkladu:<\/strong> <br \/>V soustav\u011b sou\u0159adnic Oxy je zobrazena p\u0159\u00edmka <strong><em>p<\/em><\/strong>, kter\u00e1 prot\u00edn\u00e1 sou\u0159adnicov\u00e9 osy v bodech<strong><em> M [-4; 0]<\/em><\/strong> a <strong><em>N [0; 2]<\/em><\/strong>. P\u0159\u00edmka <strong><em>q<\/em><\/strong> je rovnob\u011b\u017en\u00e1 s osou <strong><em>y<\/em><\/strong> a proch\u00e1z\u00ed bodem <strong><em>A [-6; 5]<\/em><\/strong>. P\u0159\u00edmky maj\u00ed pr\u016fnik v bod\u011b <strong><em>P<\/em><\/strong>.<\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\" wp-image-4665 aligncenter\" src=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/08\/analyticka-geometrie-priklad-1-300x202.png\" alt=\"\" width=\"444\" height=\"299\" data-mce-src=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/08\/analyticka-geometrie-priklad-1-300x202.png\" srcset=\"https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/08\/analyticka-geometrie-priklad-1-300x202.png 300w, https:\/\/studijni-svet.cz\/kurzy\/wp-content\/uploads\/2022\/08\/analyticka-geometrie-priklad-1.png 538w\" sizes=\"(max-width: 444px) 100vw, 444px\" \/><\/p>\n<p>a) Zapi\u0161te sm\u011brnicov\u00fd tvar rovnice p\u0159\u00edmky <strong><em>p<\/em><\/strong>.<br \/>b) Vypo\u010d\u00edtejte vzd\u00e1lenost bod\u016f <em><strong>O<\/strong><\/em>, <strong><em>P<\/em><\/strong> (<strong>v\u00fdsledek nezaokrouhlujte<\/strong>).<\/p>\n<p><\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p style=\"text-align: left\" data-mce-style=\"text-align: left;\"><em>a) Sm\u011brnicov\u00fd tvar p\u0159\u00edmky<\/em><br \/>1) Na z\u00e1klad\u011b p\u0159\u00edmky MN jsme schopni ur\u010dit vektor n<br \/>$$ \\rightarrow _{MN} = (4; 2)$$ $$ \\rightarrow _{n} = (2; -4)$$<br \/>2) K v\u00fdpo\u010dtu vyu\u017eijeme vzore\u010dek pro obecnou rovnici<br \/>$$ax + by + c = 0$$<br \/>3) Dosad\u00edme sou\u0159adnice A a B z p\u0159\u00edmky MN<br \/>$$2x &#8211; 4y + c = 0$$<br \/>4) Za x a y dosaz\u00edme sou\u0159adnice bodu M<br \/>$$2(-4) &#8211; 4\\cdot 0 + c = 0$$<br \/>5) Nyn\u00ed ji\u017e v\u00edme kolik je c a m\u016f\u017eeme pokra\u010dovat ve v\u00fdpo\u010dtech<br \/>$$c = 8$$<br \/>6) Znovu dosad\u00edme do obecn\u00e9 rovnice, tentokr\u00e1t obsad\u00edme i t\u0159et\u00ed nezn\u00e1mou<br \/>$$2x &#8211; 4y + 8 = 0$$<br \/>7) Celou rovnici pokr\u00e1t\u00edme 2<br \/>$$x &#8211; 2y + 4 = 0$$<br \/>8) P\u0159evedeme si do sm\u011brnicov\u00e9ho tvaru p\u0159\u00edmky<br \/>$$2y = x + 4$$<br \/>9) P\u0159epo\u010d\u00edt\u00e1me na 1 y<br \/>$$y = \\frac{1}{2} x + 2$$<br \/>&nbsp; <br \/>&nbsp; <br \/><em>b) Vzd\u00e1lenost bod\u016f O, P<\/em><br \/>1) Nejprve sestav\u00edme rovnice k z\u00edsk\u00e1n\u00ed sou\u0159adnic bod\u016f P a O<br \/>p: y &#8211; 2y + 4 = 0<br \/>q: x = -6<br \/>2) Ze soustavy p\u0159ede\u0161l\u00fdch rovnic v\u00edme<br \/>P [-6; -1]<br \/>3) D\u00e1le v\u00edme<br \/>O [0; 0]<br \/>4) K zji\u0161t\u011bn\u00ed vzd\u00e1lenosti pot\u0159ebujeme zjistit<br \/>$$\\rightarrow _{PO} $$<br \/>5) \u010c\u00edsla pod odmocninou umocn\u00edme a se\u010dteme<br \/>$$|\\rightarrow _{PO} = \\sqrt{6^{2} + 1^{2}}$$<br \/>6) Vzd\u00e1lenost bod\u016f P, O je<br \/>$$|\\rightarrow _{PO} = \\sqrt{37}$$<br \/>&nbsp; <\/p>\n<p>\u010casov\u00e1 n\u00e1ro\u010dnost: 10 minut<br \/>Jedn\u00e1 se o p\u0159\u00edklad z maturitn\u00edho testu.<\/p>\n","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-4663","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Analytick\u00e1 geometrie - p\u0159\u00edklad 1 | Studijni-svet.cz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/analyticka-geometrie-priklad-1\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Analytick\u00e1 geometrie - p\u0159\u00edklad 1 | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed p\u0159\u00edkladu: V soustav\u011b sou\u0159adnic Oxy je zobrazena p\u0159\u00edmka p, kter\u00e1 prot\u00edn\u00e1 sou\u0159adnicov\u00e9 osy v bodech M [-4; 0] a N [0; 2]. P\u0159\u00edmka q je rovnob\u011b\u017en\u00e1 s osou y a proch\u00e1z\u00ed bodem A [-6; 5]. P\u0159\u00edmky maj\u00ed pr\u016fnik v bod\u011b P. a) Zapi\u0161te sm\u011brnicov\u00fd tvar rovnice p\u0159\u00edmky p.b) Vypo\u010d\u00edtejte vzd\u00e1lenost bod\u016f O, P (v\u00fdsledek ... 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0] a N [0; 2]. P\u0159\u00edmka q je rovnob\u011b\u017en\u00e1 s osou y a proch\u00e1z\u00ed bodem A [-6; 5]. P\u0159\u00edmky maj\u00ed pr\u016fnik v bod\u011b P. a) Zapi\u0161te sm\u011brnicov\u00fd tvar rovnice p\u0159\u00edmky p.b) Vypo\u010d\u00edtejte vzd\u00e1lenost bod\u016f O, P (v\u00fdsledek ... 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