ÂºÃ°ÃÃ°Â²Ã¢Â²Ã¶Ã Ã´ÃÃÃ Ã´Ã 11

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ÜÏ. 62 ÜÏ. 63 Ð³×³Ë û·ï³Ï³ñ ¿ Ý³¨ å³ñ½»É, Ã» ýÇùëí³Í áõÕÕ³ÝÏÛáõÝ Ïááñ¹ÇÝ³ï³- ÛÇÝ Ñ³Ù³Ï³ñ·áõÙ ÇÝãå»±ë »Ý ÷á÷áËíáõÙ ïí³Í Ï»ïÇ Ïááñ¹ÇÝ³ïÝ»ñÁ Ïááñ¹ÇÝ³ïÝ»ñÇ ëÏ½μÝ³Ï»ïÇ ßáõñçÁ α ³ÝÏÛáõÝáí åïï»ÉÇë£ ¸Çóáõù M(x; y) Ï»- ïÁ O Ï»ïÇ ßáõñçÁ α ³ÝÏÛáõÝáí åïï»ÉÇë ëï³óí»É ¿ M 1 (x 1 ; y 1 ) Ï»ïÁ (ÝÏ. 63)£ Üß³Ý³Ï»Ýù OM = OM 1 = a, ÇëÏ OM Ñ³ïí³ÍÇ ¨ Ox ³é³ÝóùÇ ¹ñ³Ï³Ý áõÕ- ÕáõÃÛ³Ý Ï³½Ù³Í ³ÝÏÛáõÝÁª ϕ£ ²Û¹ ¹»åùáõÙª a · cos ϕ = x, a · sin ϕ = y, a · cos(α + ϕ) = x 1 , a · sin(α + ϕ) = y 1 £ àõëïÇª x 1 = a · cos(α + ϕ) = a cos α · cos ϕ − a sin α · sin ϕ = x cos α−y sin α y 1 = a · sin(α + ϕ) = a sin α · cos ϕ + a cos α · sin ϕ = x sin α +y cos α ²ÛëåÇëáí, M(x; y) Ï»ïÁ O Ï»ïÇ ßáõñçÁ α ³ÝÏÛáõÝáí åïï»Éáõó ëï³óí³Í M 1 (x 1 ; y 1 ) Ï»ïÇ Ïááñ¹ÇÝ³ïÝ»ñÁ M(x; y) Ï»ïÇ Ïááñ¹ÇÝ³ïÝ»ñáí ³ñï³- Ñ³ÛïíáõÙ »Ý Ñ»ï¨Û³É μ³Ý³Ó¨»ñáíª x 1 = x · cos α − y sin α y 1 = x · sin α + y cos α (1) ÜÏ³ï»Ýù, áñ ³Ûë μ³Ý³Ó¨»ñÇó Ï³ñ»ÉÇ ¿ ëï³Ý³É åïáõÛïÁ ß³ñÅáõÙ ÉÇÝ»- Éáõ ÷³ëïÇ ¨ë Ù»Ï ³å³óáõÛó£ Æñáù, ¹Çóáõù A(a, b) ¨ B(m, n) Ï»ï»ñÁ Ïááñ¹Ç- Ý³ïÝ»ñÇ O ëÏ½μÝ³Ï»ïÇ ßáõñçÁ α ³ÝÏÛáõÝáí åïï»ÉÇë ëï³óí»É »Ý Ñ³Ù³å³ï³ëË³Ý³μ³ñ A 1 (a 1 ; b 1 ) ¨ B 1 (m 1 ; n 1 ) Ï»ï»ñÁ£ Àëï (1) μ³Ý³Ó¨»ñÇª a 1 = a cos α − b sin α, b 1 = a sin α + b cos α, m 1 = m cos α − n sin α, n 1 = m sin α + n cos α àõëïÇª A 1 B 2 1 = (a 1 − m 1 ) 2 + (b 1 − n 1 ) 2 = [(a − m) cos α − (b − n) sin α] 2 + + [(a − m) sin α + (b − n) cos α] 2 = (a − m) 2 · (sin 2 α + cos 2 α) + + (b − n) 2 (sin 2 α + cos 2 α) = (a − m) 2 + (b − n) 2 = AB 2 ⇒ A 1 B 1 = AB⎦ ²ÛÅÙ å³ñ½»Ýù, Ã» ÇÝãåÇëÇ ß³ñÅáõÙ Ïëï³óíÇ »ñÏáõ Ñ³ïíáÕ ³é³ÝóùÝ»- ñáí Ñ³çáñ¹³Ï³Ý Ñ³Ù³ã³÷áõÃÛáõÝÝ»ñÇ ³ñ¹ÛáõÝùáõÙ£ ²Û¹ Ñ³ñóÇÝ å³ï³ë- Ë³ÝáõÙ ¿ Ñ»ï¨Û³É Ã»áñ»ÙÁ. 88
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