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Επαναληπτικά Θέματα και Απαντήσεις στη Τεχνολογική και Θετική Κατεύθυνση της Β΄ Λυκείου

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• 1. www.mathschool-online.com 10 1. A) ; . , . , , . ) . . : =- O www.mathschool-online.com

2. www.mathschool-online.com www.mathschool2. .r u r rr ) x = + + r u r r r ) x = + 3. : rrrr) , = r rr r) , = r r r r) = 0 , = 0 r rrr) // = , R www.mathschool-online.com www.mathschool 3. www.mathschool-online.com4. : uuur uuuruuuu OA + OB rOM = 2 , .mathschool-online.com OM : OM = OA + AM (1) OM = OB + BM (2) (1)+(2) 2 OM = OA + AM + OB + BM = OA + OB uuur uuuruuuu OA + OB rOM = 2www.mathschool-online.com 4. www.mathschool-online.comwww.mathschool 2 1) .== . : = + - +) . + ;www.mathschool-online.comwww.mathschool 5. www.mathschool-online.com : uuur uuuruuu A + r = 2 2) =(1,-1) =(1,2). -2 = :2=2(1,2)=(2,4)E: -2=(1,-1)-(2,4) = (-1, + 3) ) (1,2) (2,0). . (x,y): x1 + x 2x=2 y1 + y 2y=2 : (1,2)=(x1, y1) (2,0)=B(x2,y2)www.mathschool-online.com 6. www.mathschool-online.comE:1+ 2 3 x==2 2 2+0 2y== =12 2(x,y)=(3/2 ,1)) (-2,-1) (2,0). . x , y (x,y) : (x, y) = (x 2 , y 2 ) (x1 , y1 ) = (x 2 x1 , y 2 y1 ) : (-2,-1)= (x1, y1)(2,0)= B(x2,y2)E: (x, y) = (x 2 , y 2 ) (x1 , y1 ) = (x 2 x1 , y 2 y1 ) (x, y) = (2 ( 2), 0 (1)) = (2 + 2, +1) = (4,1)www.mathschool-online.com 7. www.mathschool-online.comM : = x + y 2 2 = 4 + 1 2 2 = 16 + 1 = 17 3 1.) : r r xy1 / / 1=0 x2 y2 (1,3)= (x1, y1) (2,6)= (x2,y2) . :1 3= 1.6 2.3 = 6 6 = 02 6 . ) : i) //xx ... =0www.mathschool-online.com 8. www.mathschool-online.com ii) //yy iii) // ... 1=2 , 1,2 , . 2.) =(-2 , 2-4) , R. i)//xx ii) = .i) //xx , . : = 0ur = 0 u r 2 4 u r = =02 2 22 u r ==02 ( 2)( + 2) u r ==0 2 u r =+2=0 + 2 = 0 = 2www.mathschool-online.com 9. www.mathschool-online.com ii) = o . : -2=0 2-4=0 . . : (1)-2= 0=2 (2) -2=0(-2)(+2)=0=2 =-2 =-2 (1) . =2. ) (1,) (3,2). // . : r r xy1 / / 1=0 x2 y2 www.mathschool-online.com 10. www.mathschool-online.com // :1 = 0 1.2 3. = 0 3 2 2 3 = 0 3 = 2 3 2 2= =3 3 33.) ; r r r r r r r r =| | | | , r r .) :r r r r r) = 0 = 0 , . =0www.mathschool-online.com 11. www.mathschool-online.comr rr r) , = 0 . rrr r r r ) , ... =| | | | .rrr rr r) , ... = | | | | . rr) 2 =| |2) A (x1, y1) (x2,y2) ...r r = x1 x 2 + y1 y 2r r) , ... 1. 2 = 1 1 , 2 ; ) (1,2)= (x1,y1) (3,1)= (x2,y2) .: x1x 2 + y1 y 2 =x1 + y1 x 2 + y 2 222 2www.mathschool-online.com 12. www.mathschool-online.comE : 1 3 + 2 1 = 1 + 2 3 +1 222251 2 ===5 102 2 = /4=2+/4 (1) =2- /4 (2) , : 0 1800 (2) : (1) =2+/4 =/4 , =0 4. (1,0)= (x1,y1) (1,1)= (x2,y2) r ur uur + . r r r r : = 0 : www.mathschool-online.com 13. www.mathschool-online.comu ur r r ( + ) = 0u ur rr ( + ) = 0 u ur r urr. + = 0 u2ru rr + = 0 u 2 rurr + = 0 (1)Y r r ur = 12 + 02 = 1u rr. = 1.1 + 0.1 = 1 : u2 rurr (1) : + = 0 12 + .1 = 0 1 + = 0 = 1 41.) (x1, y1) B(x2,y2), x1x2 www.mathschool-online.com 14. www.mathschool-online.com (x1, y1) B(x2,y2) x1x2 : y 2 y1= x 2 x1) (4,2) (6,4) 42= 64 2 = =1 2) :i) 1//2 ... 1= 2ii) 1 2 .... 1. 2 = 1) y-y0 = (x-x0) ;H y-y0=(x-x0) , (x0,y0).) www.mathschool-online.com 15. www.mathschool-online.com =-1 (x0,y0)=(2,0) :y-y0=(x-x0)y-0=-1(x-2)y = -x+2) x=x0; (x0,y0)=(5,4) x=x0 () xx. (x0,y0)=(5,4) : x = 5) y=y0; xx (x0,y0)=(-2,6) y=y0 www.mathschool-online.com 16. www.mathschool-online.com xx. xx (x0,y0)=(-2,6) : y = 52. (2,0),(-6,4) (-4,2). :i) .ii) T .iii) . i) :242 B ==4 (6) 4 + 62 B = B = 12:. = -1 .(-1) = -1 -=-1 = 1, : www.mathschool-online.com 17. www.mathschool-online.comy 0 = 1(x 2) y = x2 ii)To (x,y) : x1 + x 2x=2 24x= 2 2x= = 12 y1 + y 2y=2 0+2y= =1 2 (x,y)=M(-1,1), :y 2 y1 =x 2 x1 : (x,y)=M(-1,1)=(x2,y2)www.mathschool-online.com 18. www.mathschool-online.com (-6,4)=B(x1,y1)E:y 2 y1 =x 2 x11 4 =1 ( 6)1 4 = 1 (6) 3 3 ==1 + 65 :y - y0 = (x - x0) y-1=-3/5(x-(-1))y-1=-3/5(x+1) 3y 1 = (x + 1) 5 3 3y = x +1 5 5 3 2y= x+ 5 5iii) www.mathschool-online.com 19. www.mathschool-online.com y 2 y1= x 2 x1 : (2,0)=(x1, y1) (-4,2)=(x2, y2) :y 2 y1 =x 2 x120 =4 ( 2)2 = 4 + 22 = = 12 H . : .. = -1 .(-1) = - 1 - ..= -1 ..=1To (x,y) :(x,y)=M(-1,1)www.mathschool-online.com 20. www.mathschool-online.com : y-y0=(x-x0)y-1=1(x-(-1)) y-1=x+1y=x+2 3.)N (0,0) . : x2+y2=2 3.)N (x0,y0) . : (x-x0)2+(y-y0) 2=2 ) (0,0) : i) ( 1, 3 )ii) B(0,-4) www.mathschool-online.com 21. www.mathschool-online.com: i) x2+y2=2 (-1)2+(3)2=2 1+3=22=4=2 :x2+y2=4 ii) x2+y2=2 0+(-4)2= 2 16= 2 =16 =4 : x2+y2=16) (2,3), (0,1). :(x-x0)2+(y-y0)2=2 (x-2)2+(y-3)2= 2 (0,1) : (0-2)2+(1-3)2=24+(-2)2= 2 4+4= 2 www.mathschool-online.com 22. www.mathschool-online.com 8= 2=8:H (2,3), (0,1) : (x-2)2+(y-3)2= 8K ! http://mathschool-online.pblogs.gr/ www.mathschool-online.com