2011 Λύσεις Σχ. β&I

Ii âêˆ ôfiùâ ˆ 60æ iii âêˆ 1 ôfiùâ ˆ

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ii) Âʈ = , ÔfiÙ ˆ = 60Æ. iii) Âʈ = –1, ÔfiÙ ˆ = 135Æ. iv) Âʈ = , ÔfiÙ ˆ = 120Æ. 2. ∞Ó ı¤ÛÔ˘Ì ¢x = x 2 – x 1 Î·È ¢y = y 2 – y 1 , ¤¯Ô˘ÌÂ: i) ii) iii) iv) 3. ™Â fiϘ ÙȘ ÂÚÈÙÒÛÂȘ Ë Â͛ۈÛË Ù˘ ¢ı›·˜ Â›Ó·È Ù˘ ÌÔÚÊ‹˜ y = ·x + ‚. i) ∂Âȉ‹ · = –1 Î·È ‚ = 2, Ë Â͛ۈÛË Ù˘ ¢ı›·˜ ›ӷÈ: y = –x + 2. ii) ∂Âȉ‹ · = ÂÊ 45Æ = 1 Î·È ‚ = 1, Ë Â͛ۈÛË Ù˘ ¢ı›·˜ ›ӷÈ: y = x + 1. · = ¢y ¢x = 1 – 3 2 – 1 = –2 1 = –2. · = ¢y ¢x = 1 – 1 –1 – 2 = 0. · = ¢y ¢x = 1 – 2 2 – 1 = –1. · = ¢y ¢x = 3 – 2 2 – 1 = 1. 3 3 7 ± 9 2 = 7 ± 3 2 6.3. ∏ Û˘Ó¿ÚÙËÛË f(x) = ·x + ‚ 83
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iii) ∂Âȉ‹ Ë Â˘ı›· Â›Ó·È ·Ú¿ÏÏËÏË Ì ÙËÓ y = 2x –3 ı· ¤¯ÂÈ ›‰È· ÎÏ›ÛË Ì ·˘Ù‹, ÔfiÙ ı· Â›Ó·È · = 2. ÕÚ· Ë ˙ËÙÔ‡ÌÂÓË Â͛ۈÛË Â›Ó·È Ù˘ ÌÔÚ- Ê‹˜: y = 2x + ‚ Î·È ÂÂȉ‹ Ë Â˘ı›· ‰È¤Ú¯ÂÙ·È ·fi ÙÔ ÛËÌÂ›Ô ∞(1, 1) ı· ÈÛ¯‡ÂÈ 1 = 2 Ø 1 + ‚ ÔfiÙ ı· ¤¯Ô˘Ì ‚ = –1. ∂Ô̤ӈ˜, Ë Â͛ۈÛË Ù˘ ¢ı›·˜ Â›Ó·È y = 2x – 1. 4. Ÿˆ˜ ›‰·Ì ÛÙËÓ ¿ÛÎËÛË 2, Û fiϘ ÙȘ ÂÚÈÙÒÛÂȘ Ë Â˘ı›· ¤¯ÂÈ Û˘- ÓÙÂÏÂÛÙ‹ ‰È‡ı˘ÓÛ˘, ÔfiÙ ¤¯ÂÈ Â͛ۈÛË Ù˘ ÌÔÚÊ‹˜ y = ·x + ‚. i) ∂Âȉ‹ · = 1, Ë ˙ËÙÔ‡ÌÂÓË Â͛ۈÛË Â›Ó·È Ù˘ ÌÔÚÊ‹˜ y = x + ‚ Î·È ÂÂȉ‹ Ë Â˘ı›· ‰È¤Ú¯ÂÙ·È ·fi ÙÔ ÛËÌÂ›Ô ∞(1, 2) ı· ÈÛ¯‡ÂÈ 2 = 1 + ‚ ÔfiÙ ı· Â›Ó·È ‚ = 1. ∂Ô̤ӈ˜ Ë Â͛ۈÛË Ù˘ ¢ı›·˜ Â›Ó·È y = x + 1. ii) ∂Âȉ‹ · = –1, Ë ˙ËÙÔ‡ÌÂÓË Â͛ۈÛË Â›Ó·È Ù˘ ÌÔÚÊ‹˜ y = –x + ‚ Î·È ÂÂȉ‹ Ë Â˘ı›· ‰È¤Ú¯ÂÙ·È ·fi ÙÔ ÛËÌÂ›Ô ∞(1, 2) ı· ÈÛ¯‡ÂÈ 2 = –1 + ‚ ÔfiÙ ı· Â›Ó·È ‚ = 3. ∂Ô̤ӈ˜ Ë Â͛ۈÛË Ù˘ ¢ı›·˜ ›ӷÈ: y = –x + 3. iii) ∂Âȉ‹ · = 0, Ë Â͛ۈÛË Ù˘ ¢ı›·˜ Â›Ó·È Ù˘ ÌÔÚÊ‹˜ y = ‚ Î·È ÂÂȉ‹ Ë Â˘ı›· ‰È¤Ú¯ÂÙ·È ·fi ÙÔ ÛËÌÂ›Ô ∞(2, 1), Ë ˙ËÙÔ‡ÌÂÓË Â͛ۈÛË Â›Ó·È y = 1. iv) ∂Âȉ‹ · = –2, Ë Â͛ۈÛË Ù˘ ¢ı›·˜ Â›Ó·È Ù˘ ÌÔÚÊ‹˜ y = –2x + ‚ Î·È ÂÂȉ‹ ‰È¤Ú¯ÂÙ·È ·fi ÙÔ ÛËÌÂ›Ô ∞(1, 3) ı· ÈÛ¯‡ÂÈ 3 = –2 + ‚ ÔfiÙ ı· ›- Ó·È ‚ = 5. ∂Ô̤ӈ˜ Ë Â͛ۈÛË Ù˘ ¢ı›·˜ ›ӷÈ: y = –2x + 5.
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