Прямая на плоскости. Ч. I (90
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13. 3x + 2y − 21 = 0; 3x + 5y − 39 = 0; M |
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14.5x − 3y + 1 = 0; x − 2y − 4 = 0; M 0; 32 ;
15.2x + y − 5 = 0; 8x − 3y + 15 = 0; M 52 ; 7 ;
16.8x − 3y + 16 = 0; 2x − 5y + 4 = 0; M 72 ; 9 ;
17.x − 5y − 10 = 0; 4x + 3y + 6 = 0; M 72 ; 1 ;
18. 2x − 3y + 17 = 0; 3x + 7y − 9 = 0; M |
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19.x − 3y − 7 = 0; 12x + 5y − 2 = 0; M 92 ; 6 ;
20.3x − 5y = 0; 7x + 4y = 0; M 3; 132 ;
21.2x − 11y + 9 = 0; 4x − 5y + 1 = 0; M 292 ; 5 ;
22.3x + 8y − 7 = 0; 9x − 2y + 31 = 0; M 6; 72 ;
23. 5x + 7y − 39 = 0; x + 3y − 19 = 0; M |
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24.3x − 4y + 18 = 0; x + 2y − 4 = 0; M 3; 112 ;
25.4x − 9y − 41 = 0; 2x + y + 7 = 0; M 132 ; 2 ;
26.2x + 13y + 12 = 0; 8x − 5y + 48 = 0; M 192 ; 2 ;
27.4x − 3y + 17 = 0; 2x + 5y − 11 = 0; M −32 ; 8 ;
28. |
x − 4y − 6 = 0; |
7x + 6y + 60 = 0; |
M 9; −2 |
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29. |
5x + 3y − 2 = 0; |
3x − 7y + 34 = 0; |
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30. 7x − 8y − 18 = 0; 5x + 4y + 26 = 0; M 4; 112 :
ZADANIE 18
CDANY URAWNENIQ DWUH STORON PARALLELOGRAMMA (AW) A1x+B1y+
1= 0 I (AD) A2x + B2y + C2 = 0 I TOˆKA E(x0 ; y0) – SEREDINA STO-
RONY (SD). NAJTI URAWNENIQ OSTALXNYH STORON PARALLELOGRAMMA:
1.8x − 3y + 16 = 0; 2x − 5y + 4 = 0; E 92 ; 6 ;
1 ; 5
2.x − 5y − 10 = 0; 4x + 3y + 6 = 0; E −2 2 ;
3. 2x − 3y + 17 = 0; 3x + 7y − 9 = 0; E 92 ; 1 ;
4. x − 3y − 7 = 0; 12x + 5y − 2 = 0; |
E(−1; 11); |
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5. 3x − 5y = 0; 7x + 4y = 0; E |
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6.2x − 11y + 9 = 0; 4x − 5y + 1 = 0; E 232 ; 6 ;
7.3x + 8y − 7 = 0; 9x − 2y + 31 = 0; E 3; 192 ;
8. 5x + 7y − 39 = 0; x + 3y − 19 = 0; E |
−2 |
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9.3x − 4y + 18 = 0; x + 2y − 4 = 0; E 2; 72 ;
10.4x − 9y − 41 = 0; 2x + y + 7 = 0; E 12 ; 3 ;
11.2x + 13y + 12 = 0; 8x − 5y + 48 = 0; E 112 ; 7 ;
12.4x − 3y + 17 = 0; 2x + 5y − 11 = 0; E −112 ; 7 ;
13. |
x − 4y − 6 = 0; |
7x + 6y + 60 = 0; |
E 6; − 2 |
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14. |
5x + 3y − 2 = 0; |
3x − 7y + 34 = 0; |
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15.7x − 8y − 18 = 0; 5x + 4y + 26 = 0; E −2; 92 ;
16.x − 3y − 6 = 0; 5x + 9y + 42 = 0; E(9; −7);
17.3x + 2y + 17 = 0; 7x + y + 25 = 0; E(−4; −8);
18. |
x − 2 + 10 |
= 0 |
y = 3; E(4; 4); |
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19. |
4x + y + 16 |
= 0; |
5x − 4y − 1 = 0; |
E(4; 10); |
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20. |
5x − 3y − 2 |
= 0; |
2x + y − 3 = 0; |
E |
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21.2x − 7y + 3 = 0; x − 5y + 3 = 0; E 12 ; 1 ;
22.3x + 2y − 22 = 0; 4x + 5y − 41 = 0; E 8; 52 ;
23. |
2x − y − 7 = 0; |
x + y − 2 = 0; E |
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24. |
5x − 2y − 24 = 0; |
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3y + 2 = 0; |
E 2; |
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25. |
4x − 3y + 2 = 0; |
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5y − 17 = 0; |
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26. |
3x + 5y − 19 = 0; |
7x + 8y − 37 = 0; |
E −2 |
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5 ; 15 |
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x − 4y − 3 = 0; |
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27. |
2x + 3y + 5 = 0; |
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28.2x − 7y − 29 = 0; 2x + y + 11 = 0; E 32 ; −6 ;
29.2x − y + 4 = 0; 5x + 3y + 21 = 0; E(1; −5);
30.3x − 4y + 9 = 0; x + y − 4 = 0; E 4; 72 :
ZADANIE 19
DANY URAWNENIE STORONY (AW) A1x + B1y + C1 = 0 PARALLELOGRAMMA AWSD, URAWNENIE DIAGONALI (AS) A2x + B2y + C2 = 0 I SEREDINA E(x0 ; y0) STORONY (SD). NAJTI URAWNENIQ OSTALXNYH STO-
RON PARALLELOGRAMMA: |
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1. |
2x − y − 1 = 0; |
− 2 + 1 = 0; |
E(4; 1); |
2. |
x − y + 4 = 0; |
4x − 3y + 13 = 0; |
E(1; 6); |
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3. 2 − + 4 = 0; x − y + 1 = 0; E(1; 3);
4.3x − y + 14 = 0; 3x − 7y + 26 = 0; E(2; 2);
5.x + 2y − 7 = 0; 3x + y − 16 = 0; E 7; 52 ;
6.2x − 3y + 10 = 0; x + 2y − 23 = 0; E 132 ; 10 ;
7.x − 2y = 0; x + y − 9 = 0; E 2; 112 ;
8. 3x + 2y − 21 = 0; |
y = 6; E 7; |
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9. 5x − 3y + 1 = 0; 4x − y + 5 = 0; E |
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10. |
2x + y − |
5 = 0; |
3x − 2y + 10 |
= 0; |
E |
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11. |
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14 = 0; |
3x − 7y − 3 |
= 0; |
E(13; 7); |
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12. |
x − y + 7 = 0; x − 5y + 23 = 0; E(1; 4); |
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13. |
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31 = 0; |
5x − 9y + 77 = 0; |
E −2 |
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14.4x − 3y − 7 = 0; 3x − 2y − 4 = 0; E 12 ; −1 ;
15.2x + 7y − 1 = 0; x − 12y + 15 = 0; E 112 ; 3 :
16. 5x + y + 13 = 0; |
x − 2y − 4 = 0; |
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17. x + 3y + 4 = 0; |
3x − 2y + 1 = 0; |
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18. |
3x − 2y − 1 = 0; |
4x − |
3y − 3 = 0; E |
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19. |
3x + 5y + 10 = 0; |
x − |
13y + 18 = 0; |
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20. |
x − 4y − 1 = 0; 4x − 3y + 9 = 0; E(−4; 2); |
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21. |
7x − 2y − 13 = 0; |
2x − 3y − 11 = 0; |
E 6; −2 |
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22. 3x − 8y − 30 = 0; 7x − 3y − 23 = 0; E 1; 52 ;
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23. 11x − 2y − 9 = 0; 4x + y − 5 = 0; E |
−1; −2 |
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24.4x − 9y + 11 = 0; x − y + 4 = 0; E −72 ; 3 ;
25.2x − 3y + 16 = 0; x + 8y − 30 = 0; E 92 ; 2 ;
26.3x + 8y − 23 = 0; 2x − y + 10 = 0; E −6; 152 ;
27. |
11x − 3y − 38 = 0; 5x − 8y − 77 = 0; |
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28. x + 4y + 5 = 0; |
x − 7y − 6 = 0; E 4; |
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29. |
3x − 7y − 7 = 0; |
8x − 3y − 3 = 0; E |
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5x + 3y − 29 = 0; 4x + 3y − 28 = 0; |
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30. |
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ZADANIE 20
DANY URAWNENIE STORONY (AW) A1x + B1y + C1 = 0 PARALLELOGRAMMA AWSD, URAWNENIE DIAGONALI (AS) A2x + B2y + C2 = 0 I SEREDINA E(x0 ; y0) STORONY (WS). NAJTI URAWNENIQ OSTALXNYH STO-
RON PARALLELOGRAMMA: |
2 |
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1. 5x + y + 13 = 0; x − 2y − 4 = 0; E |
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2. x + 3y + 4 = 0; 3x − 2y + 1 = 0; E |
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3.3x − 2y − 1 = 0; 4x − 3y − 3 = 0; E 1; 12 ;
4.3x + 5y + 10 = 0; x − 13y + 18 = 0; E(4; 0);
5.x − 4y − 1 = 0; 4x − 3y + 9 = 0; E 52 ; 2 ;
6.7x − 2y − 13 = 0; 2x − 3y − 11 = 0; E 5; 52 ;
7.3x − 8y − 30 = 0; 7x − 3y − 23 = 0; E 152 ; 2 ;
26
8. 11x − 2y − 9 = 0; 4x + y − 5 = 0; E 2 |
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9. 4x − 9y + 11 = 0; x − y + 4 = 0; E |
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10. |
2x − 3y + 16 = 0; |
x + 8y − 30 = 0; |
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7 ; 9 |
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11. |
3x + 8y − 23 = 0; |
2x − y + 10 = 0; |
E |
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3 ; 7 |
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11x − 3y − 38 = 0; |
5x − 8y − 77 = 0; |
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12. |
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13.x + 4y + 5 = 0; x − 7y − 6 = 0; E 92 ; −1 ;
14.3x − 7y − 7 = 0; 8x − 3y − 3 = 0; E 5; 92 ;
15. |
5x + |
3y − 29 = 0; 4x + 3y − 28 = 0; |
E |
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16. |
x + y − 3 = 0; x − y − 1 = 0; E(2; 5); |
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17. |
6 + |
− 13 = 0; 7x − 2y − 31 = 0; |
E(4; 8); |
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18.2x − y − 3 = 0; 9x − 4y − 11 = 0; E(5; 8);
19.2x − y + 1 = 0; 2x + y − 5 = 0; E 12 ; 0 ;
20.3x + 2y − 1 = 0; x + 7y − 13 = 0; E 72 ; 0 ;
21.4x − y − 17 = 0; 3x + y − 4 = 0; E 52 ; 0 ;
22. |
2x − 7y − 29 = 0; |
3x − 4y − 11 = 0; |
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23. |
2x − 3y − 2 = 0; |
3x − 4y − 2 = 0; E |
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24. |
3x + 2y − 5 = 0; |
y = 4; E 4; |
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25. |
2x − y − 13 = 0; |
x − y − 10 = 0; E |
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26. |
2x + 5y + 2 = 0; |
3x + 4y − 11 = 0; |
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27.3x + y − 11 = 0; x = 5; E 4; 72 ;
28.4x + y − 10 = 0; x − 3y − 9 = 0; E 112 ; 1 ;
29.x + 2y − 9 = 0; x − 5y + 5 = 0; E 172 ; 2 ;
30.3x + y − 11 = 0; x − 3y + 13 = 0; E(4; 4):
ZADANIE 21
DANY URAWNENIE STORONY (AW) A1x + B1y + C1 = 0 PARALLELO- GRAMMA AWSD, URAWNENIE DIAGONALI (WD) A2x + B2y + C2 = 0 I SEREDINA E(x0 ; y0) STORONY (WS). NAJTI URAWNENIQ OSTALXNYH STO- RON PARALLELOGRAMMA:
1.3x − 2y + 1 = 0; 3x + 2y − 31 = 0; E(7; 8);
2.x + y − 1 = 0; x + 4y − 7 = 0; E(1; 6);
3.x − 5y + 17 = 0; 2x − 7y + 25 = 0; E −1; 72 ;
4.x − 3y + 17 = 0; 3x − 4y + 21 = 0; E 12 ; 5 ;
1 ; 3
5.x + 2y + 1 = 0; 3x − y + 10 = 0; E −2 2 ;
6. |
x + 3y − 11 = 0; x − 7y + 19 = 0; E(4; 4); |
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7. 5x + 3y − 7 = 0; 2x + 5y − 18 = 0; E 2 |
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8. x − 2y − 5 = 0; 2x + y − 10 = 0; E |
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9. 2x + 5y + 3 = 0; 2x + y − 9 = 0; E |
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10.x − 2y − 5 = 0; x + 4y − 11 = 0; E 6; 72 ;
11.3x − y − 4 = 0; 7x − 3y − 8 = 0; E(3; 4);
12.4x − 3y − 2 = 0; 3x − 2y − 2 = 0; E 52 ;3 ;
13.5x − y − 49 = 0; 3x − 8y − 22 = 0; E 132 ; 2 ;
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14. 4x − 5y + 18 = 0; 3x − 4y + 15 |
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15. x + y − 3 = 0; 7x − y − 5 = 0; |
E |
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16.5x + 3y − 20 = 0; 2x + 3y − 17 = 0; E 4; 32 ;
17.3x − 7y + 6 = 0; 2x + 11y − 43 = 0; E 3; 112 ;
18.x + 4y − 8 = 0; 3x + y − 24 = 0; E 192 ; 1 ;
19.11x − 3y − 47 = 0; 17x + 2y − 139 = 0; E 192 ; 7 ;
20. |
3x + 8y − 5 = 0; |
8x + 15y − 26 = 0; |
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21. |
2x − 3y + 35 = 0; |
5x + 2y − 17 = 0; |
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22.4x − 9y + 35 = 0; x − 6y + 35 = 0; E 112 ; 8 ;
23.3x − 8y − 13 = 0; x + 13y − 20 = 0; E 92 ; 3
24. 11x − 2y + 32 = 0; 18x − 5y + 80 = 0; E |
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25.7x − 2y + 22 = 0; 5x + y − 11 = 0; E 2; 192 ;
26.x − 4y + 17 = 0; y − 6 = 0; E 92 ; 7 ;
27.3x + 5y + 11 = 0; 7x − 3y − 33 = 0; E(7; −2);
28.3x − 2y − 5 = 0; x − y − 2 = 0; E 3; 32 ;
29. |
x + 3y − 14 = 0; |
4x + y − 23 = 0; |
E |
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30. |
5x + y − 14 = 0; |
6x − y − 30 = 0; |
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29
ZADANIE 22
DANY SEREDINY STORON TREUGOLXNIKA. SOSTAWITX URAWNENIQ STO-
RON:
1. |
(−1; 2); (−2; −3); (4; −2); |
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2. |
(1 3) |
(−4; −3); (3; −4); |
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(1 3) |
(5; 5); (3; 6); |
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(1; 4); (−4; 1); (−1; 0); |
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(10; 5); |
(8; −3); |
(6;3); |
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(−1; 4); (−2; −2); (1; 1); |
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(1; 9); |
(5; 8); (3; 11); |
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(−3; 4); (2; 2); (0; −1); |
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(5; 3); (8; 5); (7; 1); |
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10. (4 |
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(8 |
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(6 |
1); |
11.(6; 5); (1; 3); (3; 1);
12.(−3 1) (1; 2); (−1; −1);
13.(−5 2) (−1; −1); (−3; −4);
14.(−1 4); (3; 9); (1; 7);
15.(−7; −5); (1; 11); (5;3);
16.(3 −2); (8; −1); (6; 4);
17. (4 2) (8 5) (5 −1);
18.(1; 4); (5; 8); (3; 7);
19.(−1 4); (3; 8); (1; 2);
20.(−2; −1); (2; 4); (−1; 1);
21. |
(2 3) |
(6 1) |
(1 −1); |
22. |
(4; 7); |
(8; 8); |
(6; 4); |
23. |
(−3 2) |
(2 3) |
(−2; 0); |
24.(−2 5); (4; 6); (1; 3);
25.(−2 −1); (2; 2); (0; −4);
26.(−1; 7); (2; 8); (1; 4);
27.(4; 3); (7; 6); (5; −1);
28.(−2 1) (3; 5); (1; −1);
29.(−3; 1); (−1; −1); (1; 2);
30.(5; 7); (8; 9); (6; 5):
30
Z DANIE 23
C DANY DWE PRQMYE (AC): A1x + B1y + C1 = 0; (BD): A2x + B2y +
2 = 0 I TOˆKI P(x1; y1); Q(x2; y2); R(x3; y3); S(x4; y4); T(x5; y5):
OBOZNAˆAQ ˆEREZ AMB TOT IZ ˆETYREH UGLOW, OB AZOWANNYH DANNY- MI PRQMYMI, W KOTOROM LEVIT TOˆKA P; A ˆEREZ CMD – WERTIKALX- NYJ UGOL, USTANOWITX, W KAKIH UGLAH LEVAT OSTALXNYE TOˆKI:
1. xT−y = 0; 2x−y+5 = 0; P(1; 3); Q(5; −2); R(−1; 4); S(−2; −3); (−7; −8);
2. 3Sx + y − 5 = 0; 4x − 5y + 7 = 0; P(2; 8); Q(0; 1); R(−3; −5); (−4; −1); T(5 −3);
3. 2Sx−3y+ 10 = 0; 7x+ 8y−14 = 0; P(5; 2); Q(−2; 5); R(−3; −6); (4; −3); T(12; −1);
4. xS+ 2y − 4 = 0; 5x − 4y + 3 = 0; P(1; 1); Q(3; 8); R(−5; 3); (−4; −4); T(9; −2);
5. 3Sx − 4y + 5 = 0; x − 7y + 11 = 0; P(5; 8); Q(1; −3); R(−2; 4); (−5; −5); T(−3; 1);
6. 2Sx − 5y + 10 = 0; 3x + 2y − 6 = 0; P(2; 5); Q(6; 7); R(−5; 3); (−4; −2); T(6; 1);
7. xS− 2y + 4 = 0; 4x + y − 12 = 0; P(1; 1); Q(−1; −1); R(−2; 5); (3; 8); T(6; 2);
8. 7Sx + 2y − 14 = 0; x − y + 3 = 0; P(4; 2); Q(10; 3); R(1; 5); (−2; 4); T(−1; −2):
DANA PRQMAQ Ax+ By + C = 0 I DWE TOˆKI P(x1 ; y1) I Q(x2 ; y2): USTANOWITX, PERESEKAET LI DANNAQ PRQMAQ OTREZOK PQ ILI EGO PRO- DOLVENIE ZA TOˆKU P ILI ZA TOˆKU Q :
9. 12 |
+ |
5y − |
7 = 0; |
P(2; 7); Q(−1; 2); |
|||||
10. |
9 |
− |
12y + 2 = |
0 |
(−3 5) |
(1; 1); |
|||
11. |
4 |
− |
7 |
+ |
26 |
= |
0 |
(−3; 3); Q(−5;2); |
|
12. |
3 |
− |
4 |
− |
15 |
= |
0 |
(8 5) |
(9 2); |
13. |
7 |
+ |
2 |
− |
15 |
= |
0; |
P(3; 5); Q(2; 2); |
|
14. |
3x − |
5y + |
3 = 0; |
P(2; 4); Q(−1; 8); |
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15. |
x + 2y − 5 = 0; P(−3; 2); Q(4; 5); |
||||||||
16. |
3x + |
4y − |
11 |
= |
0; |
P(5 −3); Q(−1;2): |
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DANY ˆETYRE TOˆKI A(x1 ; y1); |
B(x2 y2); C(x3 ; y3); D(x4 ; y4): |
USTANOWITX, PRINADLEVIT LI TOˆKA M PERESEˆENIQ PRQMYH (AB) I