7.2.2 ᠪᠠᠢᠷᠢᠰᠢᠯ ᠢᠶᠠᠷ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠰᠢᠯᠵᠢᠯᠲᠡ ᠶᠢ ᠢᠯᠡᠷᠭᠡᠢᠯᠡᠬᠦ
ᠠᠯᠪᠠᠨ ᠵᠢᠷᠤᠮ ᠤᠨ ᠰᠤᠷᠭᠠᠨ ᠬᠦᠮᠦᠵᠢᠯ ᠦᠨ ᠰᠤᠷᠬᠤ ᠪᠢᠴᠢᠭ,ᠳᠣᠯᠣᠳᠤᠭᠠᠷ ᠣᠨ( ᠳᠣᠣᠷᠠᠳᠤ),,,ᠬᠢᠴᠢᠶᠡᠯᠯᠡᠭᠴᠢ᠄ ᠬᠠᠰᠪᠤᠶᠠᠨᠳᠤ,7.2.2 ᠪᠠᠢᠷᠢᠰᠢᠯ ᠢᠶᠠᠷ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠰᠢᠯᠵᠢᠯᠲᠡ ᠶᠢ ᠢᠯᠡᠷᠭᠡᠢᠯᠡᠬᠦ,1. ᠴᠡᠭ 𝐴(−2,−3) ᠶᠢ ᠪᠠᠷᠠᠭᠤᠨᠰᠢ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠪᠡᠷ 5 ᠨᠢᠭᠡᠴᠢ ᠤᠷᠲᠤ ᠰᠢᠯᠵᠢᠬᠦᠯᠦᠬᠡᠳ᠂ ᠴᠡᠭ 𝐴 1 ( ) ᠢ ᠤᠯᠤᠨᠠ᠃,2. ᠴᠡᠭ 𝐴(−2,−3) ᠶᠢ ᠵᠡᠭᠦᠨᠰᠢ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠪᠡᠷ 2 ᠨᠢᠭᠡᠴᠢ ᠤᠷᠲᠤ ᠰᠢᠯᠵᠢᠭᠦᠯᠦᠭᠡᠳ᠂ ᠴᠡᠭ 𝐴 2 ( ) ᠢ ᠤᠯᠤᠨᠠ᠃,,,,,3 , −3,−4 , −3,ᠰᠥᠪᠡᠭᠴᠢᠯᠡᠬᠦ,ᠵᠡᠬᠦᠨᠰᠢ ᠪᠠᠷᠠᠭᠤᠨᠰᠢ ᠵᠡᠷᠬᠡᠴᠡᠬᠡ ᠰᠢᠯᠵᠢᠬᠦᠯᠬᠦ ᠳᠤ᠄ ᠵᠡᠬᠦᠨᠰᠢ ᠪᠠᠨ ᠬᠠᠰᠤᠵᠤ᠂ ᠪᠠᠷᠠᠭᠤᠨᠰᠢ ᠪᠠᠨ ᠨᠡᠮᠡᠨᠠ᠂ ᠭᠤᠯᠲᠦ ᠪᠠᠢᠷᠢᠰᠢᠯ ᠨᠢ ᠬᠤᠪᠢᠷᠠᠬᠤ ᠦᠬᠡᠢ᠃,,3,5,2,4,6,−2,−3,−4,−5,−6,𝑥,3. ᠴᠡᠭ 𝐴 (−2,−3) ᠶᠢ ᠳᠡᠭᠡᠭᠰᠢ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠪᠡᠷ 4 ᠨᠢᠭᠡᠴᠢ ᠤᠷᠲᠤ ᠰᠢᠯᠵᠢᠬᠦᠯᠦᠬᠡᠳ᠂ ᠴᠡᠭ 𝐴 3 ( ) ᠢ ᠤᠯᠤᠨᠠ᠃,4. ᠴᠡᠭ 𝐴 (−2,−3) ᠶᠢ ᠲᠤᠷᠤᠭᠰᠢ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ ᠪᠡᠷ 2 ᠨᠢᠭᠡᠴᠢ ᠤᠷᠲᠤ ᠰᠢᠯᠵᠢᠬᠦᠯᠦᠬᠡᠳ᠂ ᠴᠡᠭ 𝐴 4 ( ) ᠢ ᠤᠯᠤᠨᠠ᠃,,3,5,2,4,6,−2,−3,−4,−5,−6,,,𝑥,𝑦,−2,1,−2,−5,ᠳᠡᠭᠡᠭᠰᠢ ᠳᠣᠷᠣᠭᠰᠢ ᠵᠡᠷᠬᠡᠴᠡᠬᠡ ᠰᠢᠯᠵᠢᠬᠦᠯᠬᠦ ᠳᠤ᠄ ᠳᠣᠷᠣᠭᠰᠢ ᠪᠠᠨ ᠬᠠᠰᠤᠵᠤ᠂ ᠳᠡᠭᠡᠭᠰᠢ ᠪᠠᠨ ᠨᠡᠮᠡᠨᠠ᠂ ᠬᠦᠨᠳᠡᠯᠡᠨ ᠪᠠᠢᠷᠢᠰᠢᠯ ᠨᠢ ᠬᠤᠪᠢᠷᠠᠬᠤ ᠦᠬᠡᠢ᠃,ᠶᠡᠷᠦᠡᠭᠬᠢ ᠳᠤ ᠪᠡᠨ᠂ ᠬᠠᠪᠳ᠋ᠠᠭᠠᠢ ᠶᠢᠨ ᠲᠡᠭᠰᠢ ᠦᠨᠴᠦᠭᠲᠦ ᠪᠠᠢᠷᠢᠰᠢᠯ ᠦᠨ ᠰᠢᠰᠲ᠋ᠧᠮ ᠳᠤ᠂ ᠴᠡᠭ (𝑥,𝑦) ᠶᠢ ᠪᠠᠷᠠᠭᠤᠨ ᠲᠠᠯᠠ ᠲᠠᠢᠰᠢ ( ᠪᠤᠶᠤ ᠵᠡᠬᠦᠨ ᠲᠠᠯᠠ ᠲᠠᠢᠰᠢ ) 𝑎 ᠨᠢᠭᠡᠴᠢ ᠤᠷᠲᠤ ᠵᠡᠷᠬᠡᠴᠡᠬᠡ ᠰᠢᠯᠵᠢᠬᠦᠯᠪᠠᠯ᠂ ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠰᠠᠨ ᠴᠡᠭ (𝑥+𝑎 ,𝑦) ( ᠪᠤᠶᠤ (𝑥−𝑎 ,𝑦) ) ᠶᠢ ᠤᠯᠤᠨᠠ᠃ ᠴᠡᠭ (𝑥,𝑦) ᠶᠢ ᠲᠡᠬᠡᠭᠰᠢ ( ᠪᠤᠶᠤ ᠲᠤᠷᠤᠭᠰᠢ ) 𝑏 ᠨᠢᠭᠡᠴᠢ ᠤᠷᠲᠦ ᠵᠡᠷᠬᠡᠴᠡᠬᠡ ᠰᠢᠯᠵᠢᠬᠦᠯᠪᠠᠯ᠂ ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠰᠠᠨ ᠴᠡᠭ (𝑥, 𝑦+𝑏) ( ᠪᠤᠶᠤ (𝑥, 𝑦+𝑏) ) ᠶᠢ ᠤᠯᠤᠨᠠ᠃,,ᠲᠡᠬᠡᠭᠰᠢ 𝑏 ᠨᠢᠭᠡᠴᠢ ᠤᠷᠲᠦ,ᠳᠤᠷᠤᠭᠰᠢ 𝑏 ᠨᠢᠭᠡᠴᠢ ᠤᠷᠲᠦ,ᠵᠡᠬᠦᠨ ᠲᠡᠢᠰᠢ 𝑎 ᠨᠢᠭᠡᠴᠢ ᠤᠷᠲᠦ,ᠪᠠᠷᠠᠭᠤᠨ ᠲᠡᠢᠰᠢ 𝑎 ᠨᠢᠭᠡᠴᠢ ᠤᠷᠲᠦ,ᠬᠤᠷᠢᠶᠠᠩᠭᠤᠢᠯᠠᠯ,ᠪᠠᠶᠢᠷᠢᠰᠢᠯ ᠨᠢ (−4,−1) ᠤᠨ ᠴᠡᠭ ᠢ ᠪᠠᠷᠠᠭᠤᠨᠰᠢ ᠪᠠᠨ ᠵᠡᠷᠬᠡᠴᠡᠬᠡ 2 ᠨᠢᠭᠡᠴᠢ ᠤᠷᠲᠤ ᠰᠢᠯᠵᠢᠬᠦᠯᠵᠤ᠂ ᠳᠠᠬᠢᠨ ᠳᠡᠭᠡᠭᠰᠢ ᠵᠡᠷᠬᠡᠴᠡᠬᠡ 3 ᠨᠢᠭᠡᠴᠢ ᠤᠷᠲᠤ ᠰᠢᠯᠵᠢᠬᠦᠯᠤᠨᠠ᠂ ᠲᠡᠬᠡᠪᠡᠯ ᠰᠢᠯᠵᠢᠬᠦᠯᠥᠭᠰᠡᠨ ᠦ ᠲᠠᠷᠠᠭᠠᠬᠢ ᠴᠡᠭ ᠦᠨ ᠪᠠᠶᠢᠷᠢᠰᠢᠯ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ （ ）,A.（2, 2） B.（－2,2）C.（－2, －2）D.（2,－2）,𝐵,ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠰᠠᠨ ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠯ,ᠵᠢᠷᠤᠭ ᠮᠡᠲᠦ᠂ ᠬᠡᠷᠪᠡ ᠵᠢᠰᠢᠭᠦᠯᠵᠢᠨ ABCD ᠵᠢ ᠵᠡᠭᠦᠨᠰᠢ ᠵᠡᠷᠭᠡᠴᠡᠭᠡ 2 ᠨᠢᠭᠡᠴᠢ ᠤᠷᠲᠤ ᠰᠢᠯᠵᠢᠭᠦᠯᠵᠦ᠂ ᠳᠠᠷᠠᠭᠠ ᠨᠢ ᠳᠡᠭᠡᠭᠰᠢ 3 ᠨᠢᠭᠡᠴᠢ ᠤᠷᠲᠤ ᠰᠢᠯᠵᠢᠬᠦᠯᠤᠨᠠ᠂ ᠰᠢᠯᠵᠢᠬᠦᠯᠤᠭᠰᠡ ᠤ ᠳᠠᠷᠠᠭᠠᠬᠢ ᠵᠢᠰᠢᠭᠦᠯᠵᠢᠨ ᠤ 𝐴 ′ 𝐵 ′ 𝐶 ′ 𝐷 ′ ᠦᠨ ᠵᠢᠷᠤᠭ ᠳᠦᠷᠰᠦ ᠶᠢ ᠵᠢᠷᠤᠬᠤ ᠶᠢᠨ ᠬᠠᠮᠲᠤ ᠲᠡᠭᠦᠨ ᠦ ᠡᠯᠡ ᠤᠷᠤᠢ ᠶᠢᠨ ᠴᠡᠭ ᠦᠨ ᠪᠠᠶᠢᠷᠢᠰᠢᠯ ᠢ ᠵᠢᠭᠠᠵᠤ ᠭᠠᠷᠭᠠ᠃,ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠰᠠᠨ ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠯ,A′,B′,C′,D′,𝐴′（−3, 1）,𝐵′（1 , 1）,𝐶′（2, 4）,𝐷′（−2,4）,ᠵᠢᠷᠤᠭ ᠮᠡᠲᠦ᠂ ∆𝐴𝐵𝐶 ᠶᠢᠨ ᠭᠤᠷᠪᠠᠨ ᠣᠷᠣᠢ ᠶᠢᠨ ᠴᠡᠭ ᠦᠨ ᠪᠠᠶᠢᠷᠢᠰᠢᠯ ᠨᠢ ᠲᠤᠰ ᠲᠤᠰ 𝐴 (4,3) , 𝐵 (3,1) , 𝐶 (1,2) ᠭᠤᠷᠪᠠᠨ ᠣᠷᠣᠢ ᠶᠢᠨ ᠴᠡᠭ ᠦᠨ ᠬᠥᠨᠳᠡᠯᠡᠨ ᠪᠠᠶᠢᠷᠢᠰᠢᠯ ᠡᠴᠡ ᠪᠦᠷ 6 ᠶᠢ ᠬᠠᠰᠤᠨᠠ᠃,,,ᠬᠠᠷᠠᠭᠠᠯᠵᠠᠭᠰᠠᠨ ᠪᠣᠯᠪᠠᠰᠤᠷᠠᠯ,ᠪᠤᠲᠤᠯᠬᠢᠯᠡᠵᠤ ᠦᠵᠡ᠄ ᠤᠯᠤᠭᠰᠠᠨ ∆ 𝐴 1 𝐵 1 𝐶 1 ᠪᠤᠯᠤᠨ ∆𝐴𝐵𝐶 ᠶᠢᠨ ᠶᠡᠬᠡ ᠪᠠᠭᠠ᠂ ᠬᠡᠯᠪᠡᠷᠢ ᠲᠦᠷᠰᠤ ᠪᠠ ᠪᠠᠢᠷᠢ ᠨᠢ ᠶᠠᠮᠠᠷ ᠬᠤᠯᠪᠤᠭᠲᠠᠯ ᠲᠠᠢ ᠪᠤᠢ ？,𝐴 1 −2 , 3 𝐵 1 (−3, 1) 𝐶 1 (−5, 2),𝐴 (4,3) , 𝐵 (3,1) , 𝐶 (1,2) ᠭᠤᠷᠪᠠᠨ ᠣᠷᠣᠢ ᠶᠢᠨ ᠴᠡᠭ ᠤᠨ ᠭᠤᠯᠲᠦ ᠪᠠᠶᠢᠷᠢᠰᠢᠯ ᠠᠴᠠ ᠪᠦᠷ 5 ᠶᠢ ᠬᠠᠰᠤᠨᠠ᠃ ᠬᠦᠨᠳᠡᠯᠡᠨ ᠪᠠᠶᠢᠷᠢᠰᠢᠯ ᠬᠤᠪᠢᠷᠠᠭᠠᠬᠤ ᠦᠭᠡᠢ᠂ ᠲᠤᠰ ᠲᠤᠰ ᠴᠡᠭ 𝐴 2 , 𝐵 2 , 𝐶 2 ᠦᠨ ᠪᠠᠢᠷᠢᠰᠢᠯ ᠢ ᠪᠢᠴᠢ᠃,(2),𝐴 2 4 , −2 𝐵 2 (3, −4) 𝐶 2 (1, −3),ᠪᠤᠲᠤᠯᠬᠢᠯᠡᠵᠤ ᠦᠵᠡ᠄ ᠤᠯᠤᠭᠰᠠᠨ ∆ 𝐴 2 𝐵 2 𝐶 2 ᠪᠤᠯᠤᠨ ∆𝐴𝐵𝐶 ᠶᠢᠨ ᠶᠡᠬᠡ ᠪᠠᠭᠠ᠂ ᠬᠡᠯᠪᠡᠷᠢ ᠲᠦᠷᠰᠤ ᠪᠠ ᠪᠠᠢᠷᠢ ᠨᠢ ᠶᠠᠮᠠᠷ ᠬᠤᠯᠪᠤᠭᠲᠠᠯ ᠲᠠᠢ ᠪᠤᠢ ︖,ᠵᠢᠷᠤᠭ ᠮᠡᠲᠦ᠂ ∆ABC ᠭᠤᠷᠪᠠᠨ ᠤᠷᠤᠢ ᠶᠢᠨ ᠴᠡᠭ ᠦᠨ ᠬᠥᠨᠳᠡᠯᠡᠨ ᠪᠠᠶᠢᠷᠢᠰᠢᠯ ᠡᠴᠡ ᠴᠥᠮ 6 ᠢ ᠬᠠᠰᠤᠬᠤ ᠶᠢᠨ ᠬᠠᠮᠲᠤ ᠭᠤᠯᠳᠤ ᠪᠠᠶᠢᠷᠢᠰᠢᠯ ᠡᠴᠡ ᠴᠦᠮ 5 ᠢ ᠬᠠᠰᠤᠨᠠ᠃,(3),𝐴 2 −2 , −2 𝐵 2 (−3, −4) 𝐶 2 (−5, −3),
ᠮᠣᠩᠭᠣᠯ ᠳ᠋ᠣᠺ ᠤᠨ ᠬᠥᠮᠥᠷᠭᠡ