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# Ii âêˆ ôfiùâ ˆ 60æ iii âêˆ 1 ôfiùâ ˆ

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ii) ÂÊˆ = , ÔfiÙÂ ˆ = 60Æ. iii) ÂÊˆ = –1, ÔfiÙÂ ˆ = 135Æ. iv) ÂÊˆ = , ÔfiÙÂ ˆ = 120Æ. 2. ∞Ó ı¤ÛÔ˘ÌÂ ¢x = x 2 – x 1 Î·È ¢y = y 2 – y 1 , ¤¯Ô˘ÌÂ: i) ii) iii) iv) 3. ™Â fiÏÂ˜ ÙÈ˜ ÂÚÈÙÒÛÂÈ˜ Ë ÂÍ›ÛˆÛË ÙË˜ Â˘ıÂ›·˜ Â›Ó·È ÙË˜ ÌÔÚÊ‹˜ y = ·x + ‚. i) ∂ÂÈ‰‹ · = –1 Î·È ‚ = 2, Ë ÂÍ›ÛˆÛË ÙË˜ Â˘ıÂ›·˜ Â›Ó·È: y = –x + 2. ii) ∂ÂÈ‰‹ · = ÂÊ 45Æ = 1 Î·È ‚ = 1, Ë ÂÍ›ÛˆÛË ÙË˜ Â˘ıÂ›·˜ Â›Ó·È: 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) ∂ÂÈ‰‹ Ë Â˘ıÂ›· Â›Ó·È ·Ú¿ÏÏËÏË ÌÂ ÙËÓ y = 2x –3 ı· ¤¯ÂÈ ›‰È· ÎÏ›ÛË ÌÂ ·˘Ù‹, ÔfiÙÂ ı· Â›Ó·È · = 2. ÕÚ· Ë ˙ËÙÔ‡ÌÂÓË ÂÍ›ÛˆÛË Â›Ó·È ÙË˜ ÌÔÚ- Ê‹˜: y = 2x + ‚ Î·È ÂÂÈ‰‹ Ë Â˘ıÂ›· ‰È¤Ú¯ÂÙ·È ·fi ÙÔ ÛËÌÂ›Ô ∞(1, 1) ı· ÈÛ¯‡ÂÈ 1 = 2 Ø 1 + ‚ ÔfiÙÂ ı· ¤¯Ô˘ÌÂ ‚ = –1. ∂ÔÌ¤Óˆ˜, Ë ÂÍ›ÛˆÛË ÙË˜ Â˘ıÂ›·˜ Â›Ó·È y = 2x – 1. 4. Ÿˆ˜ Â›‰·ÌÂ ÛÙËÓ ¿ÛÎËÛË 2, ÛÂ fiÏÂ˜ ÙÈ˜ ÂÚÈÙÒÛÂÈ˜ Ë Â˘ıÂ›· ¤¯ÂÈ Û˘- ÓÙÂÏÂÛÙ‹ ‰ÈÂ‡ı˘ÓÛË˜, ÔfiÙÂ ¤¯ÂÈ ÂÍ›ÛˆÛË ÙË˜ ÌÔÚÊ‹˜ y = ·x + ‚. i) ∂ÂÈ‰‹ · = 1, Ë ˙ËÙÔ‡ÌÂÓË ÂÍ›ÛˆÛË Â›Ó·È ÙË˜ ÌÔÚÊ‹˜ y = x + ‚ Î·È ÂÂÈ‰‹ Ë Â˘ıÂ›· ‰È¤Ú¯ÂÙ·È ·fi ÙÔ ÛËÌÂ›Ô ∞(1, 2) ı· ÈÛ¯‡ÂÈ 2 = 1 + ‚ ÔfiÙÂ ı· Â›Ó·È ‚ = 1. ∂ÔÌ¤Óˆ˜ Ë ÂÍ›ÛˆÛË ÙË˜ Â˘ıÂ›·˜ Â›Ó·È y = x + 1. ii) ∂ÂÈ‰‹ · = –1, Ë ˙ËÙÔ‡ÌÂÓË ÂÍ›ÛˆÛË Â›Ó·È ÙË˜ ÌÔÚÊ‹˜ y = –x + ‚ Î·È ÂÂÈ‰‹ Ë Â˘ıÂ›· ‰È¤Ú¯ÂÙ·È ·fi ÙÔ ÛËÌÂ›Ô ∞(1, 2) ı· ÈÛ¯‡ÂÈ 2 = –1 + ‚ ÔfiÙÂ ı· Â›Ó·È ‚ = 3. ∂ÔÌ¤Óˆ˜ Ë ÂÍ›ÛˆÛË ÙË˜ Â˘ıÂ›·˜ Â›Ó·È: y = –x + 3. iii) ∂ÂÈ‰‹ · = 0, Ë ÂÍ›ÛˆÛË ÙË˜ Â˘ıÂ›·˜ Â›Ó·È ÙË˜ ÌÔÚÊ‹˜ y = ‚ Î·È ÂÂÈ‰‹ Ë Â˘ıÂ›· ‰È¤Ú¯ÂÙ·È ·fi ÙÔ ÛËÌÂ›Ô ∞(2, 1), Ë ˙ËÙÔ‡ÌÂÓË ÂÍ›ÛˆÛË Â›Ó·È y = 1. iv) ∂ÂÈ‰‹ · = –2, Ë ÂÍ›ÛˆÛË ÙË˜ Â˘ıÂ›·˜ Â›Ó·È ÙË˜ ÌÔÚÊ‹˜ y = –2x + ‚ Î·È ÂÂÈ‰‹ ‰È¤Ú¯ÂÙ·È ·fi ÙÔ ÛËÌÂ›Ô ∞(1, 3) ı· ÈÛ¯‡ÂÈ 3 = –2 + ‚ ÔfiÙÂ ı· Â›- Ó·È ‚ = 5. ∂ÔÌ¤Óˆ˜ Ë ÂÍ›ÛˆÛË ÙË˜ Â˘ıÂ›·˜ Â›Ó·È: y = –2x + 5.
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