659
.pdf6.7. (5; 6), (−7; −2). |
6.8. (6; −6), (2; 1). |
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6.9. (5; −3), (−6; −2). |
6.10. (3; |
1), (−9; −5). |
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6.11. (8; |
2), (−1; −3). |
6.12. (−6; −8), (2; −4). |
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6.13. (5; −2), (1; −6). |
6.14. (−3; 4), (−1; 5). |
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6.15. (−5; |
7), (−2; 6). |
6.16. (1; −2), (3; −9). |
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6.17. (1; −6), (−2; −3). |
6.18. (−5; 3), (4; −6). |
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6.19. (−3; |
5), (2; 8). |
6.20. (1; |
3), (−4; −6). |
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6.21. (−8; |
1), (3; 5). |
6.22. (−2; −8), (1; 3). |
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6.23. (2; |
6), (−1; −2). |
6.24. (3; −8), (5; −6). |
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6.25. (−3; −5), (−4; 2). |
6.26. (1; −4), (−2; −3). |
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6.27. (2; |
3), (−9; −4). |
6.28. (−7; 1), (2; −8). |
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6.29. (6; |
−1), (−3; −4). |
6.30. (−2; −4), (6; 1). |
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6.31. (6; |
−8), (1; 2). |
6.32. (−1; −2), (3; 7). |
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6.33. (3; |
3), (−7; −5). |
6.34. (9; |
2), (−1; −4). |
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6.35. (6; |
−3), (−1; −6). |
6.36. (6; |
5), (−1; 7). |
7.Угол между двумя прямыми, заданными уравнением
сугловым коэффициентом
Задание 7. Найти угол между двумя прямыми 1 |
и 2, заданными |
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уравнением с угловым коэффициентом. |
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7.1. : = − |
8 |
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7.2. : = − |
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7.3. : = |
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7.4. : = −6 + |
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− 7. |
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7.5. : = − |
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7.6. : = |
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+ 6. |
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7.7. : = 3 + 1, |
: = |
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7.8. 1: = − |
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7.9. : = |
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7.10. : = − |
+ 8, |
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7.11. : = |
+ |
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− 2. |
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7.12. : = 9 − 7, |
: = − |
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+ 4. |
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7.13. : = − |
+ 2, |
: = −5 − 5. |
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7.14. : = − |
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+ 1, |
: = |
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7.15. : = − |
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− |
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: = − + 2. |
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7.16. : = |
− 9, |
: = − |
− 1. |
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7.17. : = 5 + 6, |
: = − |
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+ 8. |
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7.18. : = − |
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+ 3. |
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7.19. : = − |
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7.20. : = 7 + 2, |
: = − |
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7.21. : = − |
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7.22. : = − |
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+ 4. |
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7.23. : = |
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7.24. : = − |
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− 8. |
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7.25. : = − |
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: = 2 + |
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7.26. : = |
+ 7, |
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− |
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7.27. : = −8 + |
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− |
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7.28. : = − |
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− |
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7.29. : = |
− 3, |
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7.30. : = 2 + 2, |
: = − |
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7.31. : = |
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− |
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: = − |
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+ 3. |
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7.32. : = − |
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7.33. : = − |
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− |
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: = −2 + 8. |
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7.34. : = − |
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7.35. : = − |
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7.36. : = |
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+ |
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: = − |
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+ 1. |
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8. Нахождение точки пересечения двух прямых Задание 8. Найти точку пересечения двух прямых 1 и 2, заданных
общим уравнением.
8.1. 1: |
3 − 4 − |
10 = 0, |
2: + 7 + 5 = 0. |
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8.2. 1: |
2 + + 2 = 0, |
2: 4 − 5 + 32 = 0. |
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8.3. 1: |
4 + 7 − |
7 = 0, |
2: 2 − − 17 = 0. |
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8.4. 1: |
5 − 6 − |
4 = 0, |
2: 3 + − 7 = 0. |
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8.5. 1: |
5 + 4 − |
7 = 0, |
2: 11 + 2 + 5 = 0. |
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8.6. 1 |
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3 + 5 + |
14 = 0, |
2: 9 − 2 − 26 = 0. |
8.7. 1 |
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5 + 12 + 9 = 0, |
2: 6 + 7 − 4 = 0. |
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8.8. 1 |
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3 − 4 + |
7 = 0, |
2: − 11 − 17 = 0. |
8.9. 1 |
: |
2 + 5 + |
28 = 0, |
2: 4 − 3 + 4 = 0. |
8.10. 1: 6 + 17 + 13 = 0, |
2: 2 − 3 + 13 = 0. |
|||
8.11. 1: 3 + 7 + 13 = 0, |
2: 9 − 4 + 14 = 0. |
|||
8.12. 1: 8 − 3 − 5 = 0, |
2: 3 + 2 − 30 = 0. |
|||
8.13. 1: 5 − 6 − 3 = 0, |
2: 12 − 7 + 15 = 0. |
|||
8.14. 1: 14 + 5 + 5 = 0, |
2: 7 + 12 − 1 = 0. |
|||
8.15. 1: 15 + 7 + 6 = 0, |
2: 4 − 9 − 31 = 0. |
|||
8.16. 1: 9 + 4 + 4 = 0, |
2: 7 + 3 + 4 = 0. |
|||
|
|
|
|
162 |
8.17. 1: 3 − 8 − 31 = 0, |
2: 9 + 17 − 11 = 0. |
8.18. 1: 4 − 11 − 1 = 0, |
2: 5 + 2 − 17 = 0. |
8.19. 1: 10 + 7 + 3 = 0, |
2: 4 − 5 + 9 = 0. |
8.20. 1: 6 − 11 + 21 = 0, |
2: 3 − 5 + 9 = 0. |
8.21. 1: 3 − 7 − 5 = 0, |
2: 2 + 3 − 11 = 0. |
8.22. 1: 6 + 5 − 13 = 0, |
2: 4 + + 3 = 0. |
8.23. 1: 4 − 17 + 11 = 0, |
2: 2 − 9 + 5 = 0. |
8.24. 1: 3 − 10 − 12 = 0, |
2: 2 − 3 + 3 = 0. |
8.25. 1: 4 + 7 + 18 = 0, |
2: 10 − 3 + 4 = 0. |
8.26. 1: 12 − 5 − 11 = 0, |
2: 3 − 2 + 1 = 0. |
8.27. 1: 9 − 8 − 2 = 0, |
2: 5 + 2 − 14 = 0. |
8.28. 1: 6 − 11 + 7 = 0, |
2: 5 − 8 + 7 = 0. |
8.29. 1: 14 + 3 + 4 = 0, |
2: 2 − 5 − 32 = 0. |
8.30. 1: 4 + 11 − 25 = 0, |
2: + 2 − 4 = 0. |
8.31. 1: 3 − 10 − 8 = 0, |
2: 2 − 7 − 6 = 0. |
8.32. 1: 10 − 9 − 14 = 0, |
2: 5 − 9 + 11 = 0. |
8.33. 1: 4 + 9 − 1 = 0, |
2: 6 − 5 + 17 = 0. |
8.34. 1: + 3 − 3 = 0, |
2: 2 + 5 − 8 = 0. |
8.35. 1: 9 − 4 + 3 = 0, |
2: 6 − 5 + 9 = 0. |
8.36. 1: 2 − 5 − 3 = 0, |
2: 3 + 2 − 14 = 0. |
9. Расстояние от точки до прямой Задание 9. Найти расстояние от точки до прямой , заданной об-
щим уравнением.
9.1.(4; −9), : 6 + 8 − 1 = 0.
9.2.(−5; 6), : 3 − 2 + 10 = 0.
9.3.(−3; −4), : 3 − 5 + 6 = 0.
9.4.(2; 8), : 7 − − 8 = 0.
9.5.(−6; 7), : 4 − 9 − 3 = 0.
9.6.(9; −2), : 2 − 2 + 5 = 0.
9.7.(1; −3), : 5 + 2 + 4 = 0.
9.8.(−6; −5), : 11 − 3 − 4 = 0.
9.9.(−1; 7), : 2 − 4 − 3 = 0.
9.10.(3; 6), : 2 + 9 − 1 = 0.
9.11.(5; −8), : 3 + 4 − 7 = 0.
9.12.(4; −8), : 6 − 7 + 2 = 0.
9.13.(9; −2), : 2 − 7 + 3 = 0.
9.14.(3; −4), : 5 + − 8 = 0.
9.15.(2; −6), : 3 − 2 + 5 = 0.
9.16.(4; 7), : 6 + 7 − 2 = 0.
9.17.(−5; 3), : 4 − 2 + 5 = 0.
9.18.(−4; −1), : 2 − 5 + 3 = 0.
9.19.(5; −4), : 3 − 7 + 6 = 0.
9.20.(8; −7), : 4 + 5 − 8 = 0.
9.21.(6; −7), : 3 − 2 + 3 = 0.
163
9.22.(−3; 1), : 5 + 4 − 2 = 0.
9.23.(6; −2), : 5 − 2 + 3 = 0.
9.24.(−3; −2), : 7 − + 4 = 0.
9.25.(−2; 1), : 7 + 3 + 8 = 0.
9.26.(−1; −2), : + 5 − 6 = 0.
9.27.(5; 7), : 3 − 4 − 5 = 0.
9.28.(−9; 1), : 2 − 4 + 5 = 0.
9.29.(8; −8), : 2 + − 4 = 0.
9.30.(3; 7), : 5 + 5 − 4 = 0.
9.31.(5; 3), : 7 − 4 + 1 = 0.
9.32.(2; 3), : 5 − 3 − 8 = 0.
9.33.(−1; −2), : 3 + 7 + 6 = 0.
9.34.(6; 6), : − 7 + 3 = 0.
9.35.(5; −1), : 4 − 2 − 7 = 0.
9.36.(3; −5), : 6 + − 9 = 0.
Второй уровень сложности
10. Построение прямой по заданному общему уравнению Задание 10. Построить прямые, заданные общим уравнением.
10.1. 1) |
− 8 − 9 = 0; |
2) |
3 + |
4 − 1 = 0; |
||
3) 6 − 2 + 3 = 0; |
4) 2 + + 7 = 0; |
|||||
5) + = 0; |
6) 4 − 3 = 0; |
|||||
7) 5 + 6 = 0; |
8) 3 − 8 = 0; |
|||||
9) |
− 1 = 0; |
10) + 9 |
= 0. |
|||
10.2. 1) |
5 + |
2 − 3 = 0; |
2) |
4 − |
+ 8 = 0; |
|
3) − − 5 = 0; |
4) + 5 + 2 = 0; |
|||||
5) 3 − 4 = 0; |
6) 6 + 7 = 0; |
|||||
7) 3 − 2 = 0; |
8) 4 + 9 = 0; |
|||||
9) |
+ 2 = 0; |
10) − 4 = 0. |
||||
10.3. 1) |
− + 7 = 0; |
2) |
+ 3 + 4 = 0; |
|||
3) 2 − 5 − 3 = 0; |
4) 3 + 2 − 6 = 0; |
|||||
5) 5 − 2 = 0; |
6) 4 + = 0; |
|||||
7) 5 + 9 = 0; |
8) 3 − 10 = 0; |
|||||
9) |
− 3 = 0; |
10) + 5 = 0. |
||||
10.4. 1) |
8 + + 4 = 0; |
2) |
3 − 2 − 1 = 0; |
|||
3) 5 + 5 − 4 = 0; |
4) 9 − 3 + 5 = 0; |
|||||
5) + = 0; |
6) − 3 = 0; |
|||||
7) 2 + 1 = 0; |
8) 4 − 5 = 0; |
|||||
9) |
− 4 = 0; |
10) + 2 = 0. |
||||
10.5. 1) |
− 6 − 1 = 0; |
2) |
3 + 2 + 2 = 0; |
|||
3) − + 4 = 0; |
4) 7 + − 9 = 0; |
|||||
5) 6 − 7 = 0; |
6) 5 + 3 = 0; |
|||||
7) 5 − 2 = 0; |
8) 3 + 2 = 0; |
|||||
9) |
+ 5 = 0; |
10) − 8 = 0. |
||||
10.6. 1) |
+ − 2 = 0; |
2) |
− 4 + 7 = 0; |
|||
|
|
|
164 |
|
|
|
3) 2 − − 2 = 0; |
4) 3 + 4 + 1 = 0; |
|||||
5) + 5 = 0; |
6) 6 − 7 = 0; |
|||||
7) 3 + 8 = 0; |
8) 5 − 9 = 0; |
|||||
9) |
+ 2 = 0; |
10) − 3 |
= 0. |
|||
10.7. 1) |
2 − |
3 + 3 = 0; |
2) |
4 − |
− 1 = 0; |
|
3) 5 + 6 − 9 = 0; |
4) + 3 + 5 = 0; |
|||||
5) 2 − 3 = 0; |
6) + = 0; |
|||||
7) 4 − 7 = 0; |
8) 2 − 7 = 0; |
|||||
9) |
− 1 = 0; |
10) + 4 |
= 0. |
|||
10.8. 1) |
5 + |
2 + 4 = 0; |
2) |
− − 3 = 0; |
||
3) + 3 − 7 = 0; |
4) 6 − + 2 = 0; |
|||||
5) 3 + 5 = 0; |
6) 4 − 9 = 0; |
|||||
7) 3 + 2 = 0; |
8) 5 − 6 = 0; |
|||||
9) |
+ 5 = 0; |
10) − 8 |
= 0. |
|||
10.9. 1) |
− + 3 = 0; |
2) |
5 − |
3 − 2 = 0; |
||
3) + 5 − 1 = 0; |
4) 4 + + 5 = 0; |
|||||
5) 4 − 7 = 0; |
6) 2 + 5 = 0; |
|||||
7) 6 − 5 = 0; |
8) 7 + 1 = 0; |
|||||
9) |
= 0; |
10) − 5 |
= 0. |
|||
10.10. 1) |
5 − 6 + 7 = 0; |
2) |
− 2 |
− 8 = 0; |
||
3) + − 4 = 0; |
4) 5 + + 8 = 0; |
|||||
5) 3 − 7 = 0; |
6) 5 + 2 = 0; |
|||||
7) 3 − 4 = 0; |
8) 6 + 1 = 0; |
|||||
9) |
+ 4 = 0; |
10) − 6 |
= 0. |
|||
10.11. 1) |
3 + 8 + 3 = 0; |
2) |
6 − |
5 − 2 = 0; |
||
3) + 2 − 6 = 0; |
4) 7 − + 1 = 0; |
|||||
5) + = 0; |
6) 3 − 2 = 0; |
|||||
7) 5 + 1 = 0; |
8) 7 + 9 = 0; |
|||||
9) |
− 5 = 0; |
10) + 1 |
= 0. |
|||
10.12. 1) |
− + 2 = 0; |
2) |
7 − 3 − 6 = 0; |
|||
3) + 2 − 5 = 0; |
4) 8 + + 1 = 0; |
|||||
5) 4 + 3 = 0; |
6) 7 − = 0; |
|||||
7) 6 − 1 = 0; |
8) 5 + 2 = 0; |
|||||
9) |
− 9 = 0; |
10) + 2 |
= 0. |
|||
10.13. 1) |
2 + 3 + 6 = 0; |
2) 3 − − 9 = 0; |
||||
3) + 4 − 2 = 0; |
4) 6 − 7 + 6 = 0; |
|||||
5) 4 − 9 = 0; |
6) 6 + 7 = 0; |
|||||
7) 5 − 1 = 0; |
8) 3 + 8 = 0; |
|||||
9) |
− 6 = 0; |
10) + 3 |
= 0. |
|||
10.14. 1) |
9 − + 2 = 0; |
2) 5 − 3 − 8 = 0; |
||||
3) + 4 − 5 = 0; |
4) + + 2 = 0; |
|||||
5) 9 − 5 = 0; |
6) 7 + 3 = 0; |
|||||
7) 5 − 2 = 0; |
8) 7 + 3 = 0; |
|||||
9) |
+ 3 = 0; |
10) − 3 |
= 0. |
|||
10.15. 1) |
2 − 3 + 9 = 0; |
2) 5 + 4 − 4 = 0; |
||||
|
|
|
165 |
|
|
|
3) 3 + + 7 = 0; |
4) − 4 − 4 = 0; |
|||||
5) + = 0; |
6) 3 − 7 = 0; |
|||||
7) 5 − 1 = 0; |
8) 7 + 2 = 0; |
|||||
9) |
− 6 = 0; |
10) + 8 = 0. |
||||
10.16. 1) |
+ + 8 = 0; |
2) |
3 − |
2 + 6 = 0; |
||
3) + 5 − 2 = 0; |
4) 6 − − 9 = 0; |
|||||
5) 5 − 9 = 0; |
6) 3 + 2 = 0; |
|||||
7) 8 − 7 = 0; |
8) 4 + 9 = 0; |
|||||
9) |
+ 1 = 0; |
10) = 0. |
||||
10.17. 1) |
8 + |
3 − 3 = 0; |
2) |
+ 7 + 2 = 0; |
||
3) 5 − + 3 = 0; |
4) 4 − 2 − 3 = 0; |
|||||
5) 5 − 2 = 0; |
6) + = 0; |
|||||
7) 7 − 3 = 0; |
8) 5 + 9 = 0; |
|||||
9) |
− 2 = 0; |
10) + 8 = 0. |
||||
10.18. 1) |
− + 4 = 0; |
2) |
5 − |
7 − 9 = 0; |
||
3) 3 + − 1 = 0; |
4) 6 + 3 + 8 = 0; |
|||||
5) + 3 = 0; |
6) 8 − 5 = 0; |
|||||
7) 6 − 1 = 0; |
8) 3 + 7 = 0; |
|||||
9) |
+ 6 = 0; |
10) − 9 = 0. |
||||
10.19. 1) |
5 − 7 + 5 = 0; |
2) |
3 + |
− 4 = 0; |
||
3) 6 + 3 + 7 = 0; |
4) − 4 − 5 = 0; |
|||||
5) − = 0; |
6) 9 + 2 = 0; |
|||||
7) 8 − 5 = 0; |
8) 4 + 9 = 0; |
|||||
9) |
+ 7 = 0; |
10) − 4 = 0. |
||||
10.20. 1) |
+ − 6 = 0; |
2) |
3 + + 2 = 0; |
|||
3) 7 − 8 − 8 = 0; |
4) 4 − + 5 = 0; |
|||||
5) 2 + 7 = 0; |
6) 5 − 2 = 0; |
|||||
7) 3 + 2 = 0; |
8) 6 − 1 = 0; |
|||||
9) |
− 3 = 0; |
10) − 8 = 0. |
||||
10.21. 1) |
5 − 5 + 2 = 0; |
2) |
3 − − 6 = 0; |
|||
3) + 6 − 8 = 0; |
4) 7 + 2 + 2 = 0; |
|||||
5) + 4 = 0; |
6) − = 0; |
|||||
7) 3 − 5 = 0; |
8) 6 + 7 = 0; |
|||||
9) |
+ 8 = 0; |
10) + 2 = 0. |
||||
10.22. 1) |
6 + + 4 = 0; |
2) 2 − 5 − 7 = 0; |
||||
3) + 3 − 8 = 0; |
4) − + 2 = 0; |
|||||
5) 9 − 2 = 0; |
6) 8 + 3 = 0; |
|||||
7) 5 − 4 = 0; |
8) 2 − 1 = 0; |
|||||
9) |
= 0; |
10) + 5 = 0. |
||||
10.23. 1) |
− 6 − 7 = 0; |
2) 3 + 2 − 6 = 0; |
||||
3) 5 + + 9 = 0; |
4) − + 3 = 0; |
|||||
5) 7 − 3 = 0; |
6) 2 + 5 = 0; |
|||||
7) 4 − 1 = 0; |
8) 8 + 9 = 0; |
|||||
9) |
− 2 = 0; |
10) + 3 = 0. |
||||
10.24. 1) |
8 − 3 + 4 = 0; |
2) 2 − 5 − 1 = 0; |
||||
|
|
|
166 |
|
|
|
3) 9 + + 2 = 0; |
4) + 2 − 7 = 0; |
||||
5) − = 0; |
6) 5 + 2 = 0; |
||||
7) 3 − 8 = 0; |
8) 5 − 7 = 0; |
||||
9) |
+ 2 = 0; |
10) + 5 = 0. |
|||
10.25. 1) |
3 − + 1 = 0; |
2) |
+ 2 − 7 = 0; |
||
3) 6 + 4 + 9 = 0; |
4) − − 7 = 0; |
||||
5) 2 + 3 = 0; |
6) 5 − 7 = 0; |
||||
7) 9 + 1 = 0; |
8) 4 − 7 = 0; |
||||
9) |
− 8 = 0; |
10) + 3 = 0. |
|||
10.26. 1) |
8 − |
3 + 8 = 0; |
2) |
− − 2 = 0; |
|
3) 5 + − 3 = 0; |
4) 7 + 2 + 5 = 0; |
||||
5) − 4 = 0; |
6) 3 + 5 = 0; |
||||
7) 7 − 9 = 0; |
8) 6 − 5 = 0; |
||||
9) |
+ 3 = 0; |
10) − 9 = 0. |
|||
10.27. 1) |
2 − |
4 + 5 = 0; |
2) |
+ − 4 = 0; |
|
3) 2 + + 9 = 0; |
4) − 7 − 8 = 0; |
||||
5) 5 + 9 = 0; |
6) 3 − 2 = 0; |
||||
7) 3 − 7 = 0; |
8) 5 + 4 = 0; |
||||
9) |
+ 9 = 0; |
10) − 5 = 0. |
|||
10.28. 1) |
− + 3 = 0; |
2) |
6 + |
8 − 5 = 0; |
|
3) + 4 + 1 = 0; |
4) 5 − − 2 = 0; |
||||
5) 5 + 2 = 0; |
6) 3 − 4 = 0; |
||||
7) 3 + 8 = 0; |
8) 4 − 7 = 0; |
||||
9) |
− 8 = 0; |
10) = 0. |
|||
10.29. 1) |
6 − 6 − 5 = 0; |
2) |
+ 4 − 1 = 0; |
||
3) 3 − + 9 = 0; |
4) 6 + 8 + 5 = 0; |
||||
5) − = 0; |
6) 2 + 9 = 0; |
||||
7) 3 − 5 = 0; |
8) 5 − 4 = 0; |
||||
9) |
+ 2 = 0; |
10) − 7 = 0. |
|||
10.30. 1) |
+ + 8 = 0; |
2) |
3 − − 6 = 0; |
||
3) + 7 − 5 = 0; |
4) 9 − 3 + 5 = 0; |
||||
5) 4 − 7 = 0; |
6) 5 + 2 = 0; |
||||
7) 3 − 7 = 0; |
8) 4 + 2 = 0; |
||||
9) |
− 4 = 0; |
10) − 6 = 0. |
|||
10.31. 1) |
8 − + 2 = 0; |
2) − 6 − 7 = 0; |
|||
3) 8 + 3 + 7 = 0; |
4) + − 5 = 0; |
||||
5) 9 + 7 = 0; |
6) 2 − 5 = 0; |
||||
7) 4 + 3 = 0; |
8) 5 − 1 = 0; |
||||
9) |
+ 3 = 0; |
10) + 1 = 0. |
|||
10.32. 1) |
2 + + 2 = 0; |
2) − 3 − 9 = 0; |
|||
3) 7 + 2 − 3 = 0; |
4) − + 6 = 0; |
||||
5) 5 + 3 = 0; |
6) 3 − 7 = 0; |
||||
7) 5 + 2 = 0; |
8) 3 + 4 = 0; |
||||
9) |
+ 5 = 0; |
10) − 9 = 0. |
|||
10.33. 1) |
5 − 6 + 1 = 0; |
2) 3 − − 6 = 0; |
|||
|
|
|
167 |
|
|
3) + 9 − 4 = 0; |
4) + + 3 = 0; |
|||
5) 8 − 5 = 0; |
6) 3 + 4 = 0; |
|||
7) 5 + 3 = 0; |
8) 4 − 9 = 0; |
|||
9) |
+ 2 = 0; |
10) − 8 |
= 0. |
|
10.34. 1) |
− − 8 = 0; |
2) |
3 − |
+ 7 = 0; |
3) 6 + 6 − 1 = 0; |
4) + 3 + 9 = 0; |
|||
5) 4 + 3 = 0; |
6) 5 − 9 = 0; |
|||
7) 2 + 9 = 0; |
8) 4 − 5 = 0; |
|||
9) |
− 1 = 0; |
10) + 4 |
= 0. |
|
10.35. 1) |
7 − − 1 = 0; |
2) |
3 + 2 − 9 = 0; |
|
3) − 4 + 8 = 0; |
4) 5 + 4 + 2 = 0; |
|||
5) + = 0; |
6) 4 − 9 = 0; |
|||
7) 5 + 1 = 0; |
8) 3 − 7 = 0; |
|||
9) |
− 7 = 0; |
10) + 2 |
= 0. |
|
10.36. 1) |
4 + 2 − 7 = 0; |
2) + + 6 = 0; |
||
3) 8 − − 2 = 0; |
4) − 3 + 2 = 0; |
|||
5) 2 + 7 = 0; |
6) 3 − 5 = 0; |
|||
7) 9 − 2 = 0; |
8) 4 − 5 = 0; |
|||
9) |
+ 1 = 0; |
10) − 6 |
= 0. |
11. Составление уравнений сторон треугольника по данным координатам его вершин
Задание 11. Даны вершины треугольника , , . Составить уравнения сторон треугольника.
11.1.(−4; −1), (−1; 5), (3; 2).
11.2.(−5; 2), (−1; −3), (6; 3).
11.3.(2; −4), (5; 6), (7; −2).
11.4.(3; −4), (5; −2), (8; −5).
11.5.(−5; 2), (4; −3), (7; 2).
11.6.(−3; −2), (3; 6), (7; 1).
11.7.(−8; 3), (−4; 1), (−1; 5).
11.8.(2; 3), (6; −2), (7; 8).
11.9.(−3; −6), (−1; 4), (5; −2).
11.10.(−5; 8), (−2; −2), (4; 1).
11.11.(−5; −2), (3; −3), (7; 2).
11.12.(3; 2), (4; 6), (9; 1).
11.13.(2; −4), (5; 6), (8; −2).
11.14.(−8; −3), (1; 1), (7; −1).
11.15.(−6; 0), (4; 5), (7; 2).
11.16.(−2; 7), (5; 1), (8; 6).
11.17.(−3; −7), (−1; 4), (6; 2).
11.18.(−6; −9), (−5; 7), (2; 6).
11.19.(−5; 1), (−2; −2), (3; 4).
11.20.(3; −4), (5; 6), (8; 2).
11.21.(1; 3), (5; 0), (7; 8).
11.22.(1; −1), (7; 4), (9; −5).
168
11.23.(−3; 2), (4; −1), (6; 5).
11.24.(3; −2), (4; 5), (7; 1).
11.25.(−8; 2), (−5; 1), (−2; 7).
11.26.(−5; −9), (−1; 4), (5; 1).
11.27.(−2; 7), (1; 1), (8; 5).
11.28.(−6; 5), (3; −7), (5; −2).
11.29.(−4; 9), (2; 3), (6; 7).
11.30.(4; 5), (7; 7), (9; 2).
11.31.(2; 0), (5; −3), (8; 4).
11.32.(−3; −6), (2; 4), (7; 1).
11.33.(−5; 3), (2; −4), (8; 1).
11.34.(1; −2), (5; 6), (8; −1).
11.35.(3; −6), (5; 4), (8; −2).
11.36.(−3; 7), (4; −2), (9; 5).
12. Составление уравнения медианы треугольника по данным координатам его вершин
Задание 12. Даны вершины треугольника , , . Составить уравнение медианы, проведённой из вершины .
12.1.(−5; −2), (2; 4), (5; 3).
12.2.(2; 2), (6; −4), (7; 8).
12.3.(−3; −6), (−2; 4), (3; −2).
12.4.(−4; −5), (3; 6), (8; 1).
12.5.(−7; −3), (−4; 6), (−2; 1).
12.6.(3; 7), (4; 2), (8; 3).
12.7.(−5; 2), (3; 0), (4; 6).
12.8.(−3; −2), (4; −1), (7; 6).
12.9.(2; 5), (3; −4), (7; −1).
12.10.(−2; 6), (−1; −2), (3; 4).
12.11.(3; −2), (5; 6), (8; 2).
12.12.(2; 4), (5; −3), (7; 8).
12.13.(−5; −2), (3; 9), (7; 7).
12.14.(1; −1), (4; 6), (8; −3).
12.15.(3; 4), (7; 0), (8; 5).
12.16.(3; 9), (5; 1), (7; 4).
12.17.(4; 3), (6; 5), (8; −2).
12.18.(−5; −6), (0; 3), (4; −2).
12.19.(1; −2), (5; 4), (7; 3).
12.20.(2; 2), (6; 4), (7; −3).
12.21.(2; −4), (3; 6), (8; −3).
12.22.(3; 4), (5; −6), (6; −5).
12.23.(−5; −2), (1; 9), (3; 5).
12.24.(4; 2), (7; −2), (8; 4).
12.25.(1; 5), (4; −2), (7; 3).
12.26.(−2; −6), (3; 7), (6; −4).
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12.27.(−6; 8), (−3; 1), (2; 5).
12.28.(2; −2), (5; 6), (7; 3).
12.29.(−3; 4), (−1; 2), (5; 3).
12.30.(−2; −4), (1; 3), (5; 2).
12.31.(−5; 0), (2; 6), (7; −3).
12.32.(1; −2), (5; 4), (8; 2).
12.33.(−2; 6), (4; −3), (6; 2).
12.34.(−4; 3), (6; −1), (7; 2).
12.35.(−3; −4), (3; 5), (7; −2).
12.36.(2; −3), (4; 5), (8; −1).
13.Угол между двумя прямыми, заданными общим уравнением Задание 13. Найти угол между двумя прямыми 1 и 2, заданными
общим уравнением.
13.1. 1: 5 − 2 − 6 = 0, |
2: 3 + 7 − 1 = 0. |
13.2. 1: 6 − 4 + 5 = 0, |
2: + 3 − 8 = 0. |
13.3. 1: 4 + 5 − 2 = 0, |
2: 3 − 3 + 7 = 0. |
13.4. 1: 2 + 3 + 4 = 0, |
2: 6 − + 2 = 0. |
13.5. 1: 7 − 2 − 3 = 0, |
2: 5 + 6 = 0. |
13.6. 1: + 3 − 3 = 0, |
2: 6 − 4 + 1 = 0. |
13.7. 1: 2 − 3 + 2 = 0, |
2: 4 + 7 + 2 = 0. |
13.8. 1: 8 + − 8 = 0, |
2: − 2 − 4 = 0. |
13.9. 1: 4 − 6 + 3 = 0, |
2: 7 + − 1 = 0. |
13.10. 1: 3 − 5 − 2 = 0, |
2: 9 + 5 − 3 = 0. |
13.11. 1: 4 + 5 = 0, |
2: 6 − 2 − 3 = 0. |
13.12. 1: 8 − 2 − 7 = 0, |
2: + 4 + 2 = 0. |
13.13. 1: 5 − 3 + 6 = 0, |
2: 3 − 2 − 5 = 0. |
13.14. 1: − 4 + 2 = 0, |
2: 3 − 2 − 2 = 0. |
13.15. 1: 7 − − 3 = 0, |
2: 5 + 2 + 4 = 0. |
13.16. 1: 2 + 6 + 3 = 0, |
2: 3 + − 2 = 0. |
13.17. 1: 3 − 2 = 0, |
2: 4 + 5 + 3 = 0. |
13.18. 1: 4 − 7 − 2 = 0, |
2: 3 − 3 − 2 = 0. |
13.19. 1: 5 + 8 − 4 = 0, |
2: 2 − 6 + 5 = 0. |
13.20. 1: − 6 + 5 = 0, |
2: 4 + 2 − 7 = 0. |
13.21. 1: 8 − + 8 = 0, |
2: 3 + 2 + 1 = 0. |
13.22. 1: 6 + 2 + 1 = 0, |
2: 3 − 4 − 2 = 0. |
13.23. 1: 3 + 4 + 6 = 0, |
2: − 7 = 0. |
13.24. 1: 9 + 3 + 2 = 0, |
2: 3 − − 2 = 0. |
13.25. 1: 6 − 5 + 5 = 0, |
1: 4 + 2 + 7 = 0. |
13.26. 1: 2 − 2 + 3 = 0, |
2: 7 + 3 − 1 = 0. |
13.27. 1: 4 + 3 − 8 = 0, |
2: 5 − 6 + 3 = 0. |
13.28. 1: 2 − 7 + 2 = 0, |
2: 6 − 8 − 5 = 0. |
13.29. 1: 5 + 3 + 4 = 0, |
2: − 6 − 3 = 0. |
13.30. 1: − 5 − 2 = 0, |
2: 3 + 7 = 0. |
13.31. 1: 2 + 6 − 5 = 0, |
2: 6 + − 4 = 0. |
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