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ﺗﺤﻠﻴﻠﻴﺔ ﺍﻟﺠﺬﺍء ﺍﻟﺴﻠﻤﻲ ﺗﻤﺮﻳﻦ 1 ﺍﻟﻤﺴﺘﻮﻯ ) (Rﻣﻨﺴﻮﺏ ﺇﻟﻰ ﻡ.ﻡ.ﻡ ) ) A (- 1,1 ﻧﻌﺘﺒﺮ ﺍﻟﻨﻘﻂ : ­1ﺃﺣﺴﺐ: ­2 ­3 AB . AD , j ) B (- 1 , 3 ﻭ (O, i ) C (- 4 , 4 ﻭ ) ﻭ D (1 , 1 ﻭ ) E (- 4 , - 2 ﻭ ٬ BC . DEﻣﺎﺫﺍ ﺗﺴﺘﻨﺘﺞ ؟ ﺑﻴﻦ ﺃﻥ (BE ) ^ (CD) : ﺑﻴﻦ ﺃﻥ ( AM ) ^ (BC ) :ﺣﻴﺚ Mﻣﻨﺘﺼﻒ ] [DE ﺗﻤﺮﻳﻦ 2 ﺍﻟﻤﺴﺘﻮﻯ ) (Rﻣﻨﺴﻮﺏ ﺇﻟﻰ ﻡ.ﻡ.ﻡ ) (O, i , j ﻧﻌﺘﺒﺮ ﺍﻟﻨﻘﻂ A(1 ; 1 ) : ­1ﺑﻴﻦ ﺃﻥ ABCﻣﺜﻠﺚ ﻗﺎﺋﻢ ﺍﻟﺰﺍﻭﻳﺔ ﻓﻲ A ) B (1 ; 3 ﻭ ­2ﺃ­ ﺃﺣﺴﺐ : ﺏ­ ﺃﺣﺴﺐ : CA CB ﻭ CA. CB ) ﻭ ﻭ ) C (- 1 ; 1 ) ﻭ ( D 0 ; 1+ 3 CD ﻭ CA.CD ) ( ) ( ) (CA, CBﻭ )(CA, CD ( ) ( ﺝ­ ﺃﺣﺴﺐ cos CA, CB :ﻭ sin CA, CBﻭ cos CA, CDﻭ sin CA, CD ﺩ­ ﺍﺳﺘﻨﺘﺞ ﻗﻴﺎﺳﻲ ﺍﻟﺰﺍﻭﻳﺘﻴﻦ : ­3ﺗﺤﻘﻖ ﺃﻥ: (CB, CD ) = 12p p ­4ﺍﺳﺘﻨﺘﺞ ﺣﺴﺎﺏ: 12 Cos ﻭ p 12 Sin ﺗﻤﺮﻳﻦ 3 ﺍﻟﻤﺴﺘﻮﻯ ) (Rﻣﻨﺴﻮﺏ ﺇﻟﻰ ﻡ.ﻡ.ﻡ ) , j ﻧﻌﺘﺒﺮ ﺍﻟﻨﻘﻂ A(2 , 2 ) :ﻭ ) B (- 1,1 ­1ﺃﻧﺸﺊ ﺍﻟﻨﻘﻂ Aﻭ Bﻭ C (O, i ﻭ ) C (0 , - 1 ­2 ﺃ­ ﺃﻭﺟﺪ ﻣﻌﺎﺩﻟﺔ ﺍﻟﻤﺴﺘﻘﻴﻢ ) (Dﺍﻟﻤﺎﺭ ﻣﻦ Bﻭ ﺍﻟﻌﻤﻮﺩﻱ ﻋﻠﻰ ) . ( AC ﺏ­ ﺣﺪﺩ ﻣﻌﺎﺩﻟﺔ ﺩﻳﻜﺎﺭﺗﻴﺔ ﻟﻠﻤﺴﺘﻘﻴﻢ ) ( AC ﺝ­ ﺣﺪﺩ ﺯﻭﺝ ﺇﺣﺪﺍﺛﻴﺘﻲ Hﻧﻘﻄﺔ ﺗﻘﺎﻃﻊ ) (Dﻭ ) ( AC ) ( ­3ﺍﺣﺴﺐ cos CA. CB ­4ﺣﺪﺩ ﻣﻌﺎﺩﻟﺔ ﺩﻳﻜﺎﺭﺗﻴﺔ ﻟﻠﻤﺴﺘﻘﻴﻢ ) (Lﻭ ﺍﺳﻂ ﺍﻟﻘﻄﻌﺔ ][AB 1/2 ﺗﻤﺮﻳﻦ 4 ﺍﻟﻤﺴﺘﻮﻯ ) (Rﻣﻨﺴﻮﺏ ﺇﻟﻰ ﻡ.ﻡ.ﻡ ) ) ﻧﻌﺘﺒﺮ ﺍﻟﻨﻘﻂ : ­1ﺑﻴﻦ ﺃﻥ ( A 1, 2 3 ABC ) ﻭ ) , j ( B 0, 3 (O, i ﻭ ﻣﺘﺴﺎﻭﻱ ﺍﻟﺴﺎﻗﻴﻦ ﻓﻲ ﺍﻟﻨﻘﻄﺔ ( ) ) C (1, 0 B ( ­2ﺃﺣﺴﺐ Cos BA, BC :ﻭ tan BA, BC ­3ﺣﺪﺩ ﻣﻌﺎﺩﻟﺔ ﺩﻳﻜﺎﺭﺗﻴﺔ ﻟﻼﺭﺗﻔﺎﻉ ﺍﻟﻤﻨﺸﺄ ﻣﻦ ﺍﻟﻨﻘﻄﺔ Bﻟﻠﻤﺜﻠﺚ ABC ­4ﺣﺪﺩ ﻣﻌﺎﺩﻟﺔ ﺩﻳﻜﺎﺭﺗﻴﺔ ﻟﻠﻤﺘﻮﺳﻂ ﺍﻟﻤﺎﺭ ﻣﻦ ﺍﻟﻨﻘﻄﺔ Cﻟﻠﻤﺜﻠﺚ ABC ­5ﺣﺪﺩ ﺇﺣﺪﺍﺛﻴﺘﻲ Gﻣﺮﻛﺰ ﺛﻘﻞ ﺍﻟﻤﺜﻠﺚ ABC ­6ﺍﺣﺴﺐ ﻣﺴﺎﺣﺔ ﺍﻟﻤﺜﻠﺚ ABC ­7ﺃ­ ﺣﺪﺩ ﻣﻌﺎﺩﻟﺔ ﺩﻳﻜﺎﺭﺗﻴﺔ ﻟﻠﻤﺴﺘﻘﻴﻢ ) (BC ﺏ­ ﺃﺣﺴﺐ ﻣﺴﺎﻓﺔ Aﻋﻦ ﺍﻟﻤﺴﺘﻘﻴﻢ ) (BC ﺗﻤﺮﻳﻦ 5 ﺍﻟﻤﺴﺘﻮﻯ ) (Rﻣﻨﺴﻮﺏ ﺇﻟﻰ ﻡ.ﻡ.ﻡ ) ﻧﻌﺘﺒﺮ ﺍﻟﻤﺴﺘﻘﻴﻢ: ) (D ﺍﻟﻤﺎﺭ ﻣﻦ , j (O, i ) A( - 1 ; 0ﺣﻴﺚ ) u ( 2 ; 4ﻣﻨﻈﻤﻴﺔ ﻋﻠﻴﻪ ﻭ ﻧﻌﺘﺒﺮ ﺍﻟﻤﺴﺘﻘﻴﻢ (D ) : 2 x = y + 4 ­1 ﺣﺪﺩ ﻣﻌﺎﺩﻟﺔ ﺩﻳﻜﺎﺭﺗﻴﺔ ﻟـ ) (D ﺑﻴﻦ ﺃﻥ ) (D ) ^ (D ­3 ﺣﺪﺩ ﻣﺴﺎﻓﺔ ﺍﻟﻨﻘﻄﺔ Aﻋﻦ ) (D ­4 ﺃﻭﺟﺪ ﺇﺣﺪﺍﺛﻴﺘﻲ Hﺍﻟﻤﺴﻘﻂ ﺍﻟﻌﻤﻮﺩﻱ ﻟﻠﻨﻘﻄﺔ Aﻋﻠﻰ ) (D ﺃﺣﺴﺐ ﺑﻄﺮﻳﻘﺔ ﺃﺧﺮﻯ ﻣﺴﺎﻓﺔ ﺍﻟﻨﻘﻄﺔ Aﻋﻦ ) (D ­2 ­5 ﺗﻤﺮﻳﻦ 6 ﺍﻟﻤﺴﺘﻮﻯ ) (Rﻣﻨﺴﻮﺏ ﺇﻟﻰ ﻡ.ﻡ.ﻡ ) ﻧﻌﺘﺒﺮ ﺍﻟﻨﻘﻂ : ) A( 1 ; - 2ﻭ ) B (2 , 0 wﺃﻭﺟﺪ ﺇﺣﺪﺍﺛﻴﺘﻲ H , j ﻭ (O, i ) C ( -1 , - 4 ﻣﺮﻛﺰ ﺗﻌﺎﻣﺪ ﺍﻟﻤﺜﻠﺚ ABC 2/2