,.,. 7 86
0 70 7 7 7 74 75 76 77 78 79 70 7 7 7 75 74 7 7 7 70 79 78 77 76 75 74 7.,. x, x A(x ), B(x ) x x AB =x -x A{x } B{x } x >x AB =x -x B{x } A{x } x =[ -x(xæ0) -x (x<0) A(x ), B(x ) AB = x -x, O(0)A(x ) OA = x A, B A(), B(7) A(), B(-7) A(-), B(7) A(-), B(-7) 87
0 O, A. A (6, ),. y O B 4 5 6 A x. A x B, B.. O, B A, B.. OAB O, A. A(x, y ), B(x, y ). ABC y y B{x,`y } AB =AC +BC y A{x,`y } C{x,`y }, O x x x AC = x -x, BC = y -y AB =(x -x ) +(y -y ) AB ="( x -x ) +(y -y ) 88
. A(x, y ), B(x, y ) AB =" (x -x ) +(y -yç ), O(0, 0)A(x, y ) OA =" x +y A(, -5), B(-4, ) y P B{-4,} y O P{0,a} x P (0, a) AP =BP "( 0-) +(a+5) ="( 0+4) +(a-) 9+a +0a+5=6+a -4a+4 4a=-4 a=- A{,-5} P (0, -) O(0, 0), A(-4, ) A(7, ), B(-5, -) A(-5, ), B(0, -) x P 89
`:`8`, :8. :8,., :8. :8,,. :8. :8, :8.,. :8. 90
0 AP =x, PB = AB :AP =AP :PB (x+) : x=x : x -x-=0 '5 x=, x>0 +'5 :. AB AB :AP =AP :PB P AB.,, 8:5.. A P B. AB m n P A P B AP :PB =m : n (m>0, n>0), P AB m:n, P AB AB =8-=5 AP :PB =m:n m 5m AP = AB = 5m x=+ap =+ x= 8 A(), B(8) m n AB m:n P(x) A{} P{x} B{8} AP =x-, PB =8-x, AP :PB =m : n (x-) : (8-x)=m :n m(8-x)=n(x-), ()x=8 x= 8 P { 8 } 9
x <x<x m n A{x } P{x} B{x } x <x<x n m B{x } P{x} A{x } A(x ), B(x ) AB m:n P mx +nx P { } (, m>0, n>0), m=npab, x +x P { } A(), B() AB M(x) AB : P(x) + x= =7 + x= =8 + AM =x-, BM =-x AM :BM =: (x-) : (-x)= : x-=-x, x=4 A{} x=7 M{x} B{} MM(7) AP =x-, BP =-x AP :BP =: (x-) : (-x)= : x-4=6-x, 5x=40 A{} x=8 P{x} B{} PP(8) A, B AB : P A(-), B(4) A(-4), B() 9
A D B E C ABCª DBE BD :DA =BE :EC A(, ), y B{7,`8} 8 B(7, 8) AB m:n H n P(x, y) y G P{x,`y} m A, P, B x F A{,`} C, D, E C D E O x 7 x D CE m:n 7 x=, A, P, B y F, G, H GFH m:n 8 y= 7 8 P {, } A(x, y ), B(x, y ) AB m:n P mx +nx my +ny P {, } (, m>0, n>0), m=n PAB, x +x y +y P {, } A(-, ), B(, ) AB : P(x, y) + (-) + 5 x= =, y= = + 4 + P {;4!;, ;%;} 9
B A G C,. A(x, y ), B(x, y ), C(x, y ) ABC G x +x +x y +y +y G{, } BC M x +x y +y M{, } G(x, y)am : x +x _+x x +x +x x= = + y +y _+y y +y +y y= = + A{x,`y } M B{x,`y } G{x,`y} O x +x +x y +y +y GG{, } y C{x,`y } x A(6, 7), B(-4, ) ABM AB : P ABC, ABC G A(0, 0), B(-6, ), C(, 4) A(-, ), B(-, ), C(, -6) 94
0 Q A, B 7`m, A B Q :. 7m,.. AQ :BQ =: AB :BQ. AB =7 m AQ, BQ AB : AB m n Q A B Q AQ :BQ =m : n (m>0, n>0, ), QAB m:n, QAB. AQ :BQ =m:n AB :BQ =() : n AB =7 7:BQ =() : n 7n BQ = x=9+bq x= 9 A(), B(9) AB m:n Q(x). m>n, x>9 m n AQ =x-, BQ =x-9, AQ :BQ =m:n (x-) : (x-9)=m : n A{} B{9} Q{x} m(x-9)=n(x-), ()x=9 x= 9 95
m<n, x< m n AQ =-x, BQ =9-x, AQ :BQ =m:n Q{x} A{} (-x) : (9-x)=m : n 9 x= 9, Q { }. B{9}. AB m:n AB m:n n -n. A(x ), B(x ) AB m:n Q mx -nx Q{ }(, m>0, n>0, ) A(-), B() AB : Q(x) - (-) x= =;&; - AQ =x+, BQ =x-, AQ :BQ =: (x+) : (x-)= : A{-} B{} Q{x} x-6=x+ x=;&; Q(x)Q{;&;} A(-), B() AB : Q AB : R 96
A D B E C ABCª DBE BA :BD =BC :BE A(, ), B(4, 5) y Q{x,`y} y AB m:n H m n 5 Q(x, y). G B{4,`5} A, B, Q x F A{,`} C, D, E E CD m:n C D E 4 O 4 x x x=, A, B, Q y F, G, H H FG m:n 5 y= 4 5 Q {, }.. A(x, y ), B(x, y ) AB m:n Q mx -nx my -ny Q {, } (, m>0, n>0, ) A(, ), B(, 4) AB : Q(x, y) - 4- x= =7, y= =8 Q(7, 8) - - A(6, 7), B(-4, ) AB : Q AB : R 97
A(), B(-) A(-), B(-5) O(0, 0), A(-, 4) P(, 0), Q(-, 6) A(-, -), B(, ), C(5, 0) ABC.. ABC. A(-, -5), B(, ) AB : P AB : Q 4 A(-, 7), B(-5, ), C(a, -) ABC G (-, b), a, b. 5 50 kg 00 kg. A B C D,. 98