ᠳᠣᠯᠣᠳᠤᠭᠠᠷ ᠪᠥᠯᠥᠭ ᠬᠠᠪᠲᠠᠭᠠᠢ ᠶᠢᠨ ᠲᠡᠭᠰᠢ ᠥᠨᠴᠥᠭᠳᠥ ᠪᠠᠢᠷᠢᠰᠢᠯ ᠤᠨ ᠰᠢᠰᠲ᠋ᠧᠮ （ᠨᠢᠭᠡᠴᠢ ᠶᠢᠨ ᠪᠠᠢᠴᠠᠭᠠᠯᠲᠠ 2） .pdf

ᠲᠤᠯᠤ ᠳ᠋ᠤᠭᠠ ᠷ ᠪᠤᠯᠦᠭ ᠦᠨ ᠪ ᠠᠶᠢᠴ ᠠᠭᠠᠯᠳ᠋ ᠠ ᠠᠩᠭᠢ ᠪᠥᠯ ᠥᠭ᠄ ᠨᠡᠷ ᠡ᠄ ︵90 ᠮᠢᠨᠦ᠋ ᠲ᠂ ᠨᠠᠢᠲᠡ 12 0 ᠬ ᠤᠪᠢ ︶ ᠨᠢᠭᠡ᠂ ᠰᠤᠩᠭᠤᠬ ᠤ ᠰᠡ ᠲᠤᠪ ᠃ ︵ ᠰᠡᠲ ᠤᠪ ᠪ ᠦᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨᠠᠢᠲᠡ 30 ᠬᠤ ᠪᠢ ︶ 1. ᠦᠭ ᠬᠦᠭᠳᠡᠭᠰᠡᠨ ᠨᠢ ᠴᠡᠭ A （2𝑎 ＋1,2 ＋𝑎 ） ᠨᠢ ᠨᠢᠭᠡᠳᠦᠭᠡᠷ ᠮᠦ᠋ᠴᠠ ᠳᠤ ᠪᠤᠢ᠂ ᠲᠡᠭᠡᠪ ᠠᠯ 𝑎 ᠤᠨ ᠭᠡᠮᠵᠢ ᠭᠳᠡᠯ ᠪᠣᠯᠬᠣ ᠪᠤᠯᠤᠯᠴᠠ ᠭ ᠠ ᠦᠭᠡᠢ ᠨᠢ ( ) A. 1 B. 0 C. − 1 D. 2 2. ᠵᠢᠷᠤᠭ 1 ᠮᠡᠳᠤ ᠂ ᠪᠢᠴ ᠢᠬᠠᠨ ᠭᠠᠷ ᠦᠨ ᠲᠤᠤ ᠷᠠᠬᠢ ᠴᠡᠭ ᠦᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠪᠣᠯᠬᠤ ᠪᠤᠯᠤᠯᠴᠠ ᠭ ᠠ ᠲᠡᠢ ᠨᠢ ( ) A. ( −4 ,− 6) B. ( −6 ,3) C. ( 5,2 ) D. ( 3, −4 ) 3. ᠲᠡᠭᠰᠢ ᠦᠠᠴᠦᠭᠳ ᠦ ᠪ ᠠᠶᠢᠷᠢᠰᠢᠯ ᠦᠨ ᠰᠢᠰᠲ᠋ ᠧᠮ ᠳᠤ ᠂ ᠴᠡ ᠭ A ( 2,1 ) ᠢᠢ ᠲᠤᠷ ᠤᠭᠰ ᠢ 2 ᠨᠢᠭᠡᠴᠢ ᠣᠷᠳ ᠤ ᠵᠡ ᠷᠭᠡᠴᠡᠭᠡ ᠰᠢᠯᠵ ᠢᠬᠦᠯᠵ ᠤ ᠂ ᠲᠠᠬᠢᠭᠠ ᠳ ᠵᠡᠬᠦᠨ ᠲᠠᠯ ᠠ ᠲᠡᠶᠢᠰᠢ 4 ᠨᠢ ᠭᠡᠴᠢ ᠤᠷᠳ ᠤ ᠵᠡ ᠷᠭᠡᠴᠡᠭ ᠡ ᠰᠢᠯᠵ ᠢᠬᠦᠯᠤ ᠭᠡᠳ ᠤᠯ ᠤᠭᠰ ᠠᠠ ᠴᠡ ᠭ ᠦ ᠨ ᠪ ᠠᠶᠢᠷᠢᠰᠢᠯ ᠨᠢ ( ) A. ( 4,3 ) B. ( −2 ,− 1) C. ( 4, −1 ) D. ( −2 ,3) 4.ᠭᠡᠷ ᠪᠡ ᠴᠡᠭ P （𝑚 ,1 − 2𝑚 ） ᠤ ᠬᠦ ᠨᠳᠡᠯᠡᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠪᠠ ᠭᠤᠤ ᠯᠳᠤ ᠪᠠ ᠶᠢᠷᠢᠰᠢᠯ ᠨᠢ ᠬᠠᠷᠢᠯ ᠴᠠᠠ ᠡᠰ ᠡᠷᠬᠦ ᠲᠣᠭ ᠠ ᠪᠣᠯ P ᠨᠢ ᠯᠠᠪᠳ ᠡᠢ ( ) ᠮᠦ᠋ ᠴᠠ ᠳᠤ ᠤᠷ ᠤᠰᠢᠨ ᠠ ᠃ A. ᠨᠢᠭᠡᠳ ᠤᠭᠡᠷ B. ᠬᠤᠶ ᠠᠳᠤᠭᠠ ᠷ C. ᠭᠤᠷᠪ ᠠᠳᠤᠭᠠ ᠷ D. ᠲᠦ᠋ ᠷᠪᠡᠳ ᠦᠭᠡᠷ 5. ᠦᠭ ᠬᠦᠭᠳ ᠡᠭᠰᠡᠨ ᠨᠢ ᠴᠡ ᠭ A （𝑚 − 1 , 𝑚 + 4 ） ᠨᠢ 𝑦 ᠲᠡᠩᠭᠡᠯ ᠢᠭ ᠲᠡᠭᠡᠷ ᠠ ᠪᠤᠢ ᠂ ᠲᠡ ᠭᠡᠪᠠᠯ ᠴᠡᠭ A ᠦᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠨᠢ ( ) A. (0 ,3) B. (0 ,5) C. (5 ,0) D. (3 ,0) 6. ᠵᠢᠷᠤᠭ 2 ᠮᠡᠳᠤ ᠂ ᠲ ᠦ᠋ᠷᠪᠡ ᠯᠵᠢᠯ ᠡᠭᠡᠰᠤ ᠲᠡᠢ ᠴᠠᠭᠠᠰᠤᠨ ᠲᠡ ᠭᠡᠷ ᠠ ᠭᠡᠷᠪᠡ ᠴᠡᠭ A , B ᠦᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ A （0,2 ） , B( 1,1 ) ᠪᠣᠯ ᠴᠡᠭ C ᠦᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠨᠢ ( ) A. (− 1,2 ) B. (2 ,− 1) C. (− 2,1 ) D. (1 ,− 2) 7. ᠲᠡᠭᠰᠢ ᠦᠠᠴᠦᠭᠳ ᠦ ᠪ ᠠᠶᠢᠷᠢᠰᠢᠯ ᠦᠨ ᠰᠢᠰᠲ᠋ ᠧᠮ ᠳᠤ᠂ ᠴᠡ ᠭ ( −1 , 𝑚 2+ 1) ᠨᠢ ᠯᠠᠪᠳ ᠡᠢ ( ) ᠮᠦ᠋ᠴᠠ ᠳᠤ ᠤᠷ ᠤᠰᠢᠨ ᠠ ᠃ A. ᠨᠢᠭᠡᠳ ᠤᠭᠡᠷ B. ᠬᠤ ᠶᠠᠳᠤᠭᠠ ᠷ C. ᠭᠤᠷᠪ ᠠᠳᠤᠭᠠ ᠷ D. ᠲᠦ᠋ᠷᠪ ᠡᠳᠦᠭᠡᠷ 8. ᠭᠡᠷᠪᠡ ᠴᠡᠭ M （− 3𝑚 − 1 , − 2𝑚 ） ᠡᠴᠠ ᠂ 𝑥 ,𝑦 ᠲᠡᠩᠭᠡᠯ ᠢᠭ ᠬᠦ ᠷᠬᠦ ᠵᠡᠢ ᠨᠢ ᠠ ᠳᠠᠯᠢ ᠪᠣᠯ 𝑚 ᠦᠨ ᠭᠡᠮᠵᠢᠭᠳ ᠡᠯ ᠨᠢ ( ) A. −1 B. 1 C. − 15 D. − 15 ᠪᠤ ᠶᠤ − 1 9. ᠵᠢᠷᠤᠭ 3 ᠮᠡᠳᠤ ᠂ ᠨᠢᠭᠡ ᠰᠢᠳ ᠠᠷ ᠡ ᠢᠢᠨ ᠤᠷᠤ ᠯᠳᠤᠭᠠ ᠨ ᠳ ᠤ ᠬᠠᠷ ᠠ ᠶᠢᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠨᠢ （B, 2 ） ᠴᠠ ᠭᠠᠨ ② ᠦᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠨᠢ ( D, 1) ᠂ ᠲᠡᠭᠡᠪ ᠠᠯ ᠴᠠ ᠭᠠᠨ ⑨ ᠢᠢᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠨᠢ ( ) A. ( C, 5) B. ( C, 4) C. ( 4, C) D. ( 5, C) 10 . ᠵᠢᠷ ᠤᠭ 4 ᠮᠡᠳᠤ ᠂ ᠲᠡ ᠭᠰᠢ ᠦᠠᠴᠦ ᠭᠳᠦ ᠢᠢᠨ ᠡᠯ ᠡ ᠲᠡᠯ ᠠ ᠨᠢ ᠬᠤᠶ ᠠᠷ ᠪ ᠠᠶᠢᠷᠢᠰᠢᠯ ᠦᠨ (1) (2) (3) ᠲᠡᠩᠭᠡᠯ ᠢᠭ ᠲᠡᠢ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠂ ᠠ ᠂ ᠡ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ ᠴᠡᠭ A (2 ,0) ᠡᠴᠠ ᠵᠡᠷᠭᠡ ᠪᠠᠷ ᠭᠠᠷᠴᠤ ᠂ ᠲᠡ ᠭᠰᠢ ᠦᠠᠴᠦ ᠭᠳᠦ ᠢᠢᠨ ᠲᠠᠯ ᠠ ᠲᠠᠭ ᠤ ᠬᠦ ᠳᠡᠯᠭᠡ ᠭᠡᠨ ᠬᠢᠨ ᠡ ᠃ ᠭᠡᠬᠦ ᠳᠦ ᠪᠡᠠ ᠠ ᠨᠢ ᠴᠠ ᠭ ᠦ ᠨ ᠵᠡ ᠬᠦᠦ ᠢᠢᠨ ᠡᠰᠡᠷ ᠬᠦ ᠴᠢᠭᠯᠡᠯ ᠢᠢᠡᠷ ᠨᠢᠭᠡ ᠨᠢᠭᠡᠴᠢ ᠢᠢᠨ ᠬᠤᠷᠳ ᠤᠴᠠ ᠪᠠᠷ ᠬᠦᠳ ᠡᠯᠭᠡᠭᠡᠨ ᠬᠢᠵ ᠤ ᠂ ᠡ ᠨᠢ ᠴᠠ ᠭ ᠦ ᠨ ᠵᠡᠬᠦᠦ ᠢᠢᠨ ᠲᠠᠭ ᠤ ᠴᠢᠭᠯᠡᠯ ᠢᠢᠡᠷ ᠬ ᠤᠶᠠᠷ ᠨᠢ ᠭᠡᠴᠢ ᠢᠢᠨ ᠬᠤᠷᠳ ᠤᠴᠠ ᠪᠠᠷ ᠬᠦᠳ ᠡᠯᠭᠡᠭᠡᠨ ᠬᠢᠨ ᠡ ᠃ ᠡᠨᠡ ᠬᠤᠶ ᠠᠷ 2 012 ᠤᠳ ᠠᠭ ᠠ ᠠᠭᠤᠯᠵᠠᠬᠤ ᠴᠡᠭ ᠦᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠨᠢ ( ) A. ( 2,0 ) B. ( −1 ,1) C. ( −2 ,1) D. ( −1 ,− 1) ᠬᠣᠶ ᠠᠷ᠂ ᠬᠠᠭ ᠠᠯᠲᠠ ᠳᠤ ᠲᠠᠭᠯ ᠠᠬᠤ ᠰᠡᠲᠤᠪ ᠃ ︵ᠰᠡᠲᠤᠪ ᠪᠦ ᠷᠢ 3 ᠬᠤᠪᠢ᠂ ᠨᠠᠢᠲ ᠡ 2 4 ᠬᠤᠪᠢ ︶ 11 . ᠨᠢ ᠭᠡ ᠺᠢᠨᠣ᠋ ᠢᠢᠨ ᠪᠢᠯᠧᠲ ᠲᠡ ᠭᠡᠷ ᠠ ᠂ 8 ᠮᠦ᠋ᠷ ᠦᠨ 4 ᠡᠭᠨᠡᠭᠡ ᠢᠢ （8, 4 ） ᠭᠡᠵ ᠤ ᠲᠡᠮᠳ ᠡᠭᠯᠡᠪ ᠡᠯ （10 ,15 ） ᠨᠢ __ __ __ __ __ __ __ __ __ __ _ ᠢ ᠯᠡᠷᠭᠡᠶᠢᠯᠡᠨ ᠡ ᠃ 12. ᠴᠡᠭ P （ －5, 1 ） ᠡᠴᠠ 𝑥 ᠲᠡ ᠩᠭᠡᠯ ᠢᠭ ᠬᠦ ᠷᠬᠦ ᠵᠡ ᠢ ᠨᠢ ___ __ 13 . ᠵᠢᠷ ᠤᠭ 5 ᠮᠡᠳᠤ ᠂ ᠤᠷ ᠳᠤ ᠲᠦ᠋ᠷᠪ ᠠᠯᠵᠢᠨ AB OC ᠳᠤ ᠴᠡᠭ A ᠢᠢᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠨᠢ ( –2 ,1) ᠲᠡᠭᠡᠪ ᠠᠯ ᠲᠡ ᠬᠦᠨ ᠦ ᠲᠠᠯᠠᠪ ᠠᠢ ᠨᠢ __ __ _ 14 . ᠭᠡᠷ ᠪᠡ ᠴᠡᠭ P (a − 1, a+ 1) ᠡᠴᠠ 𝑥 ᠲᠡ ᠩᠭᠡᠯ ᠢᠭ ᠬᠦᠷᠬᠦ ᠵᠡᠢ ᠨᠢ 3 ᠪᠣᠯ ᠲᠡᠬᠦ ᠨ ᠡᠴᠠ 𝑦 ᠲᠡᠩᠭ ᠡᠯᠢᠭ ᠬᠦᠷ ᠬᠦ ᠵᠡ ᠢ ᠨᠢ __ __ __ _ 15 . ᠭᠡᠷ ᠪᠡ ᠴᠡᠭ A ᠢᠢᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ (𝑥 ,y) ᠨᠢ (𝑥 − 3) 2+ |𝑦 + 2| = 0 ᠨᠦ᠋ᠬᠦᠴᠠ ᠯ ᠢ ᠬᠠᠩᠭ ᠠᠪᠠᠯ ᠴᠡᠭ A ᠨᠢ _ __ __ _ ᠮᠦ᠋ᠴᠠ ᠳᠤ ᠤᠷ ᠤᠰᠢᠨ ᠠ ᠃ 16 . ᠲᠡ ᠭᠰᠢ ᠦᠠᠴᠦᠭᠳᠦ ᠪᠠᠢᠷ ᠢᠰᠢᠯ ᠤᠨ ᠰᠢᠰᠲ᠋ ᠧᠮ ᠳᠤ᠂ ᠦᠭ ᠬᠦᠭᠳᠡ ᠭᠰᠡᠨ ᠨᠢ ᠭᠡᠷ ᠴᠢᠮ AB ᠶᠢᠨ ᠬᠤᠶ ᠠᠷ ᠦᠵ ᠡᠬᠦᠷ ᠤᠨ ᠴᠡᠭ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ A (− 2,6 )᠂ B( 0, −4 )᠃ ᠴᠡ ᠭ C ᠨᠢ ᠭᠡᠷᠴᠢᠮ AB ᠶᠢᠨ ᠲᠣᠮᠳ ᠡ ᠴᠡ ᠭ᠂ ᠭᠡᠷᠴᠢ ᠮAB ᠶᠢ ᠪᠠᠷ ᠠᠭᠤᠠᠰᠢ 3 ᠨᠢ ᠭᠡᠴᠢ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠰᠢᠯᠵ ᠢᠬᠦᠯᠪᠠ ᠯ ᠴᠡᠭ C ᠤᠨ ᠬᠠᠷᠠᠭ ᠠᠯᠵᠠᠭᠰᠠ ᠠ ᠴᠡ ᠭ ᠤ ᠨ ᠪ ᠠᠢᠷᠢᠰᠢᠯ ᠨᠢ_ __ __ __ _ 17 . ᠲᠡ ᠭᠰᠢ ᠦᠠᠴ ᠦᠭᠳᠦ ᠪᠠᠢᠷ ᠢᠰᠢᠯ ᠤ ᠨ ᠰ ᠢᠰᠲ᠋ ᠧᠮ ᠳᠤ ᠂ y ᠲᠡᠩᠭᠡᠯ ᠢᠭ ᠲᠡᠭᠡᠷ ᠠ ᠪ ᠠᠶᠢᠬᠤ ᠮᠦ᠋ᠷᠳ ᠡᠭᠡᠨ ᠴᠡᠭ A （0, 1 ） ᠲᠡ ᠢ 2 ᠨᠢᠭᠡᠴᠢ ᠵᠡᠶᠢᠳ ᠡᠢ ᠴᠡ ᠭ ᠦ ᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠨᠢ _ __ __ __ 18 . ᠵᠢᠷ ᠤᠭ 6 ᠮᠡ ᠳᠤ ᠂ ᠲᠡ ᠭᠰᠢ ᠦᠠᠴᠦ ᠭᠳᠦ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠦᠨ ᠰᠢᠰᠲ᠋ ᠧᠮ ᠳᠤ ᠨᠢᠭᠡ ᠴᠡᠭ ᠡᠬᠢᠨ ᠤ ᠴᠡ ᠭ O ᠡᠴᠠ ᠵᠢᠷᠤᠭ ᠮ ᠡᠳᠤ ᠬ ᠦᠳᠡᠯᠭᠡᠭᠡᠨ ᠬᠢᠨ ᠡ ᠃ ᠣ ᠯᠬᠤ ᠴᠡ ᠭ ᠦ ᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠨᠢ A 1 (0 ,1) , A 2 (1 ,1) , A 3 (1 ,0) , A 4 (2 ,0) ,… ᠲᠡᠭᠡᠪ ᠠᠯ ᠴᠡ ᠭ A 2015 ᠦᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠨᠢ _ __ __ __ _ ᠭᠤᠷᠪ ᠠ᠂ ᠪᠣᠳᠣᠵ ᠤ ᠬᠠᠷ ᠢᠭᠤᠯ ᠬᠤ ᠰᠡ ᠲᠤᠪ᠃ ( ᠨᠠ ᠢᠲᠡ 66 ᠬᠤᠪᠢ ) 21 .( 8 ᠬᠤᠪᠢ ) ᠲᠡ ᠭᠰᠢ ᠦᠠᠴ ᠦᠭᠳᠦ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠦᠨ ᠰᠢᠰᠲ᠋ ᠧᠮ ᠳᠤ ᠴᠡᠭ A( 5,1 ) , B( 5,0 ) , C( 2,1 ) , D( 2,3 ) ᠢ ᠣᠯᠵ ᠤ ᠲᠠ ᠷᠠᠭ ᠠ ᠨᠢ ᠡᠳᠡᠭᠡ ᠷ ᠴᠡ ᠭ ᠢ ᠲᠠᠰ ᠲᠠᠷᠠᠭ ᠠᠯᠠᠠ ᠬᠤᠯ ᠪᠤᠨ ᠠ ᠃ ᠮᠦ᠋ᠷᠳ ᠡᠭᠡᠨ ᠤᠯᠤᠭᠰ ᠠᠠ ᠵᠢᠷᠤᠭ ᠢ ᠲᠤᠷ ᠤᠭᠰ ᠢ 4 ᠨᠢᠭᠡᠴᠢ ᠤᠷᠳ ᠤ ᠵᠡ ᠷᠭᠡᠴᠡᠭᠡ ᠰᠢᠯᠵ ᠢᠬᠦᠯᠵ ᠤ ᠤᠯᠤᠭᠰ ᠠᠠ ᠵᠢᠷ ᠤᠭ ᠲᠥ ᠷᠰᠤ ᠶᠢᠨ ᠬᠠᠷᠠᠭ ᠠᠯᠵᠠᠭᠰᠠᠠ ᠣᠷ ᠣᠢ ᠶᠢᠨ ᠴᠡᠭ ᠦᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠢ ᠨᠢ ᠪᠢᠴ ᠢᠵᠤ ᠭᠠᠷ ᠭ ᠠ ᠃ (4) (5) (6) 22 .(1 0 ᠬ ᠤᠪᠢ ) ᠵᠢᠷ ᠤᠭ ᠮᠡᠳᠤ ᠂ ᠡᠨᠡ ᠪᠣᠯ ᠨᠢᠭᠡᠨ ᠬᠤᠳ ᠠ ᠢᠢᠨ ᠳᠦ᠋ᠬᠦ ᠮ ᠵᠢᠷ ᠤᠭ ᠪᠤᠯᠤᠨ ᠠ ᠃ (1) ᠭᠠᠯᠳ ᠤ ᠲᠡ ᠷᠭᠡᠨ ᠦ ᠦᠷᠲᠡᠭᠡ ᠪᠠᠷ ᠡᠬᠢᠨ ᠦ ᠴᠡ ᠭ ᠪᠤᠯ ᠭᠠᠨ ᠲᠡ ᠭᠰᠢ ᠦᠠᠴ ᠦᠭᠳᠦ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠦᠨ ᠰᠢᠰᠲ᠋ ᠧᠮ ᠪᠠᠶᠢᠭ ᠤᠯ ᠃ (2) ᠭᠡᠳᠤ ᠲᠡᠯᠭᠡᠬᠦᠷ ᠦᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠢ ᠪᠢᠴ ᠢ ᠃ (3) ᠲᠠᠮᠢᠷ ᠦᠨ ᠲᠠᠯᠠ ᠪᠤᠷ ᠂ ᠪᠠᠭ ᠤᠳᠠᠯ ᠂ ᠭᠠᠯᠳ ᠤ ᠲᠡ ᠷᠭᠡᠨ ᠦᠷᠲᠡᠭᠡ ᠢᠢ ᠭᠤᠷᠪ ᠠᠨ ᠴᠡ ᠭ ᠪ ᠠᠷ ᠦᠵ ᠡᠵᠤ ᠬᠤᠯ ᠪᠤᠪᠠᠯ ∆AB C ᠢᠢ ᠤᠯᠤᠨ ᠠ ᠃ ∆ AB C ᠢᠢ ᠲᠤᠷ ᠤᠭᠰ ᠢ 4 ᠨᠢ ᠭᠡᠴᠢ ᠤᠷ ᠳᠤ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠰᠢᠯᠵ ᠢᠬᠦᠯᠵ ᠤ ᠵᠢᠷ ᠤᠭᠠᠳ ᠲᠡᠬ ᠦᠨ ᠦ ᠲᠠᠯᠠ ᠪᠠᠢ ᠢᠢ ᠣ ᠯ ᠃ 23. (10 ᠬᠤᠪᠢ ) ᠲᠡ ᠭᠰᠢ ᠦᠠᠴᠦᠭᠳ ᠦ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠦᠨ ᠰᠢᠰᠲ᠋ ᠧᠮ ᠳᠦ ᠂ ∆AB C ᠢᠢᠨ ᠭᠤᠷᠪ ᠠᠨ ᠤᠷᠤᠢ ᠢᠢᠨ ᠴᠡᠭ ᠦᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ A( 0,0 ) , B( 6,0 ) , C( 5,5 ) (1) ᠭᠤᠷᠪ ᠠᠯᠵᠢ ᠨ AB C ᠶᠢᠨ ᠲᠠᠯ ᠠᠪᠠᠢ ᠢᠢ ᠣ ᠯ ᠃ (2) ᠭᠡᠷᠪᠡ ∆AB C ᠢᠢ ᠲᠡᠭᠡᠭᠰ ᠢ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ 3 ᠨᠢᠭᠡᠴᠢ ᠤᠷ ᠳᠤ ᠰᠢᠯᠵ ᠢᠬᠦᠯᠪᠠ ᠯ ∆A 1 B 1 C 1 ᠢᠢ ᠤᠯ ᠤᠨ ᠠ ᠃ ᠲᠡ ᠬᠢᠭᠠ ᠳ ᠪᠠᠷᠠᠭ ᠤᠨ ᠲᠠᠯ ᠠ ᠲᠡᠶᠢᠰᠢ ᠪᠡᠠ 2 ᠨᠢ ᠭᠡᠴᠢ ᠤᠷ ᠳᠤ ᠵᠡ ᠷᠭᠡᠴᠡᠭᠡ ᠰᠢᠯᠵ ᠢᠬᠦᠯᠪᠠ ᠯ ∆ A 2 B 2 C 2 ᠢᠢ ᠤᠯᠤᠨ ᠠ ᠃ ᠡᠨᠡ ᠬᠤᠶ ᠠᠷ ᠭᠤᠷᠪ ᠠᠯᠵᠢᠨ ᠢ ᠵᠢᠷᠤᠭᠠ ᠳ ᠪᠠᠰᠠ ∆A 2 B 2 C 2 ᠢᠢᠨ ᠭᠤᠷᠪ ᠠᠨ ᠤᠷ ᠤᠢ ᠢᠢᠨ ᠴᠡᠭ ᠦᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠢ ᠪᠢᠴ ᠢᠵᠤ ᠭᠠᠷ ᠭ ᠠ ᠃ 24 .(10 ᠬᠤᠪᠢ ) ᠵᠢᠷ ᠤᠭ ᠮᠡᠳᠤ A( −1 ,0) , C (1 , 4 ) ᠂ ᠴᠡᠭ B ᠨᠢ 𝑥 ᠲᠡᠩᠭᠡᠯ ᠢᠭ ᠲᠡᠭᠡᠷ ᠠ ᠪᠠᠶᠢᠬᠤ ᠮᠦ᠋ᠷᠳ ᠡᠭᠡᠨ AB = 3 (1) ᠴᠡᠭ B ᠦᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠢ ᠣ ᠯ ᠃ ᠪᠠᠰᠠ △ AB C ᠢᠢ ᠵᠢᠷᠤ (2) ∆AB C ᠢ ᠢᠨ ᠲᠠ ᠯᠠᠪᠠᠢ ᠢᠢ ᠣ ᠯ ᠃ 25 .(10 ᠬᠤᠪᠢ ) ᠵᠢᠷᠤᠭ ᠮᠡᠳ ᠤ ᠂ ᠨᠢᠭᠡ ᠠ ᠬᠤᠷᠤ ᠬᠠᠢ ᠲᠦ᠋ ᠷᠪᠡᠯ ᠵᠢᠯᠡᠭᠡ ᠰᠤ ᠲᠤᠤᠷ ᠲᠤᠳ ᠤᠷ ᠠ ᠬᠦᠳ ᠡᠯᠭᠡᠭᠡᠨ ᠬᠢᠨ ᠡ ᠃ ᠲᠡᠷ ᠡ A ᠡᠴᠠ ᠬᠦᠳ ᠡᠯᠵᠤ B , C , D ᠳᠤ ᠤᠴᠢ ᠨ ᠡ ᠃ ᠭᠡᠬᠦ ᠳᠦ ᠪ ᠠᠡ ᠲᠡᠭᠡ ᠭᠰᠢ ᠂ ᠪᠠᠷᠠᠭ ᠤᠨᠰᠢ ᠶᠠᠪᠤᠬ ᠤ ᠢᠢ ᠡᠶᠡᠷᠬ ᠦ ᠪ ᠠᠷ ᠠᠪᠴᠤ ᠂ ᠲᠤᠷ ᠤᠭᠰᠢ ᠪᠤ ᠶᠤ ᠵᠡᠬᠦᠨᠰ ᠢ ᠶᠠᠪᠤ ᠬᠤ ᠢᠢ ᠰᠦ᠋ᠭᠡᠷ ᠬᠦ ᠪ ᠠᠷ ᠲᠡᠮᠲᠡᠭᠯᠡᠨ ᠡ ᠃ ᠲᠠ ᠷᠤᠢ A ᠡᠴᠠ B ᠬᠦᠷᠬ ᠦ ᠢᠢ (+ 1, +4 ) ᠭᠡᠵ ᠤ ᠂ ᠨᠢᠭᠡᠳ ᠦᠭᠡᠷ ᠲᠣᠭ ᠠ ᠨᠢ ᠵᠡᠬᠦ ᠨ ᠪᠠᠷᠠᠭ ᠤᠠᠰᠢ ᠂ ᠬᠤ ᠶᠠᠳᠤᠭᠠ ᠷ ᠲᠣᠭ ᠠ ᠨᠢ ᠲᠡᠭᠡᠭᠰᠢ ᠲᠤᠷ ᠤᠭᠰᠢ ᠢᠢ ᠢᠯᠡᠷᠭᠡ ᠶᠢᠯᠡᠨ ᠡ ᠃ (1) ᠵᠢᠷᠤᠭ ᠲᠦ ᠂ (2) ᠭᠡᠷ ᠪᠡ ᠡᠨᠡ ᠬᠤᠷᠤᠬ ᠠᠢ ᠨᠢ A → B→ C→ D ᠪᠠᠷ ᠶᠠᠪᠤᠭᠰ ᠠᠠ ᠪ ᠣᠯ ᠲᠡ ᠬᠦᠨ ᠦ ᠵᠠ ᠮ ᠢ ᠪᠤᠳᠤ ᠃ (3 ) ᠭᠡᠷᠪᠡ ᠵᠢᠷᠤᠭ ᠲᠦ ᠪᠠᠰᠠ ᠬᠤᠶ ᠠᠷ ᠴᠡᠭ M ᠂ N ᠮᠦ᠋ᠷᠳ ᠡᠭᠡᠨ ᠂ ᠂ ᠲᠡ ᠭᠡᠪᠠᠯ ᠢ ᠲᠡᠮᠲᠡᠭᠯᠡᠪ ᠡᠯ ︖ 26 . (10 ᠬᠤᠪᠢ ) ᠵᠢᠷ ᠤᠭ ᠮᠡᠳᠤ ᠂ ∆ AB C ᠨᠢ ᠲᠡᠭ ᠰᠢ ᠦᠠᠴᠦᠭᠳ ᠦ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠦᠨ ᠰᠢᠰᠲ᠋ ᠧᠮ ᠳᠤ ᠪ ᠤᠢ ᠃ (1) ∆AB C ᠭᠤᠷᠪ ᠠᠨ ᠣ ᠷᠣᠢ ᠢᠢᠨ ᠴᠡᠭ ᠦᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠢ ᠪᠢᠴ ᠢ ᠃ (2) S ∆AB C ᠲᠠ ᠯᠠᠪᠠᠢ ᠢᠢ ᠣ ᠯ ᠃ (3) ∆AB C ᠢᠢ ᠲᠡᠭᠡᠭᠰ ᠢ 2 ᠨᠢᠭᠡᠴᠢ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠰᠢᠯ ᠵᠢᠬᠦ ᠯᠵᠤ ᠂ ᠲᠠ ᠷᠠᠭ ᠠ ᠨᠢ ᠪ ᠠᠷᠠᠭ ᠤᠠᠰᠢ ᠪᠠᠡ 2 ᠨᠢ ᠭᠡᠴᠢ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠰᠢᠯ ᠵᠢᠬᠦ ᠯᠦᠭᠰᠡᠨ ᠦ ᠳᠠ ᠷᠠᠭᠠ ᠬᠢ ᠵᠢᠷᠤᠭ ᠢ ᠨᠢ ᠵᠢᠷ ᠤ᠂ ᠪᠠᠰᠠ ᠡᠯ ᠡ ᠤᠷᠤᠢ ᠢᠢᠨ ᠴᠡᠭ ᠦᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠢ ᠨᠢ ᠣᠯ ᠵᠤ ᠪᠢᠴᠢ ᠃ 来 27 .(8 ᠬᠤᠪᠢ ) ᠦᠭ ᠬᠦᠭᠳ ᠡᠭᠰᠡᠨ ᠨᠢ ∆ AB C ᠶᠢᠨ ᠭ ᠤᠷᠪᠠᠨ ᠤᠷᠤᠢ ᠢᠢᠨ ᠴᠡᠭ ᠨᠢ ᠲᠦ᠋ᠷᠪ ᠡᠯᠵᠢ ᠯᠡᠭᠡᠰᠤ ᠢᠢᠨ ᠤᠭᠳ ᠤᠯᠤᠯ ᠴᠠᠯ ᠦᠨ ᠴᠡᠭ ᠲᠡ ᠭᠡᠷ ᠠ ᠪᠠᠶᠢᠨ ᠠ ᠃ ᠡᠬᠦᠨ ᠳᠦ A (3 ,3) , B( 3,5 ) ᠂ S ∆AB C = 2 ᠲᠡ ᠭᠡᠪᠠᠯ ᠴᠡᠭ C ᠦᠨ ᠪᠠᠶᠢᠷ ᠢᠰᠢᠯ ᠢ ᠣ ᠯ ᠃ ____) (_ __ _, C B ⎯ → ⎯ _____), 1 _____( + ⎯ → ⎯ C )4 , 3( − − ⎯ → ⎯ b a A M )2 , 5( − − ⎯ → ⎯ b a N M A N⎯ →⎯