เรขาคณิตวิเคราะห์ · 2017-03-18 ·...

เรขาคณตวเคราะห

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áºº½ƒ¡ËÑ ·Õè 1 (ÃÐÂÐË‹Ò§ÃÐËÇ‹Ò§¨Ø ÊÍ§¨Ø ) 1. ¨§ËÒÃÐÂÐÃÐËÇ‹Ò§ Ø´µ‹Íä»¹Õé¡Ñº Ø´¡íÒà¹Ô (0, 0)

1.1. (3, 4)

1.2. (-3, 4)

1.3. (6, 8) 2. ¨§ËÒÃÐÂÐ·Ò§ÃÐËÇ‹Ò§ Ø´áµ‹ÅÐ¤Ù‹ã¹áµ‹ÅÐ¢ŒÍµ‹Íä»¹Õé

2.1. (1, 0) áÅÐ (5, 0)

2.2. (-5, 0) áÅÐ (4, 0)

2.3. (-8, 0) áÅÐ (4, 0)


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3. ¶ŒÒÃÐÂÐË‹Ò§ÃÐËÇ‹Ò§ Ø´ (x, 3) áÅÐ (4, 7) à·‹Ò¡Ñº 5 Ë¹‹ÇÂ ¨§ËÒ¤‹Ò¢Í§ x2+1 4. ¶ŒÒÃÐÂÐÃÐËÇ‹Ò§ Ø´ (1, y) ¡Ñº (7, 10) à»š¹ÊÍ§à·‹Ò¢Í§ÃÐÂÐÃÐËÇ‹Ò§ Ø´ (3, 4) áÅÐ (6,

8) áÅŒÇ ¨§ËÒ y2+1 àÁ×èÍ y à»š¹àÅ¢ËÅÑ¡à´ÕÂÇ 5. ¨§ËÒ¾Ô¡Ñ´¢Í§ P(x, 3) «Öè§Ë‹Ò§¨Ò¡ Ø´ Q(10, 12) à»š¹ÃÐÂÐ·Ò§ 15 Ë¹‹ÇÂ


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6. ¨§ËÒ Ø´«Öè§ÍÂÙ‹º¹á¡¹ Y áÅÐÍÂÙ‹Ë‹Ò§¨Ò¡ Ø´ (2, 5) áÅÐ (3, -7) à»š¹ÃÐÂÐ·Ò§à·‹Ò¡Ñ¹ 7. Ø´ÂÍ´ÁØÁ¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ´ŒÒ¹à·‹Ò 2 Ø´ ¤×Í (0, 0) áÅÐ (0, 4) ¨§ËÒ¾×é¹·Õè¢Í§ÃÙ»

ÊÒÁàËÅÕèÂÁ´ŒÒ¹à·‹ÒÃÙ»¹Õé 8. Ç§¡ÅÁÃÙ»Ë¹Öè§ÁÕ Ø´ÈÙ¹Â�¡ÅÒ§·Õè Ø´ (5, 7) áÅÐ¼‹Ò¹ Ø´ (2, 11) ¨§ËÒ¤ÇÒÁÂÒÇ¢Í§ÃÑÈÁÕÇ§¡ÅÁ

¹Õé


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9. ¶ŒÒ Ø´ P(4, y) ÍÂÙ‹Ë‹Ò§¨Ò¡ Ø´ A(-5, 2) áÅÐ B(13, -6) à»š¹ÃÐÂÐ·Ò§à·‹Ò¡Ñ¹ ¨§ËÒ¤‹Ò y

10. §áÊ´§Ç‹Ò Ø´ (1, 1), (-1, -1) áÅÐ (-4, 1) à»š¹ Ø´ÂÍ´¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁÁØÁ©Ò¡ËÃ×ÍäÁ‹ 11. ¶ŒÒ D(-4, 2) à»š¹ Ø´áÂ‹§Ê‹Ç¹¢Í§àÊŒ¹µÃ§·Õèàª×èÍÁ Ø´ A(-8, 4) áÅÐ B(2, -1) ¨§ËÒ

ÍÑµÃÒÊ‹Ç¹áº‹§¢Í§ AD:DB


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áºº½ƒ¡ËÑ ·Õè 2 (¨Ø ¡Öè§¡ÅÒ§ÃÐËÇ‹Ò§¨Ø ÊÍ§¨Ø ) 1. ¨§ËÒ Ø´¡Öè§¡ÅÒ§ÃÐËÇ‹Ò§ Ø´áµ‹ÅÐ¤Ù‹µ‹Íä»¹Õé

1.1. (0, 0) áÅÐ (6, 8)

1.2. (1, 2) áÅÐ (7, 6)

1.3. (-3, 4) áÅÐ (5, -6) 2. ¶ŒÒÊ‹Ç¹¢Í§àÊŒ¹µÃ§ P1(x1, y1), P2(x2, y2) µÑ´á¡¹ x ·Õè Ø´ A(3, 0) áÅÐµÑ´á¡¹ y ·Õè

Ø´ B(0, 4) ¶ŒÒ Ø´ A áÅÐ B áº‹§Ê‹Ç¹àÊŒ¹µÃ§ P1P2 ÍÍ¡à»š¹ 3 Ê‹Ç¹à·‹Òæ¡Ñ¹ ¨§ËÒ P1(x1, y1) áÅÐ P2(x2, y2)


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3. ¡íÒË¹´ A(-3, 1), B(5, 7) áÅÐ C(1, 11) à»š¹ Ø´ÂÍ´ÁØÁ¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ ABC ¨§ËÒØ´»ÅÒÂ¢Í§àÊŒ¹ÁÑ¸Â°Ò¹¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ ABC ÃÙ»¹Õé

4. ¡íÒË¹´ A(1, 4), B(2, -2) áÅÐ C(8, 4) à»š¹ Ø´ÂÍ´ÁØÁ¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ ABC ¨§ËÒ

¤ÇÒÁÂÒÇ¢Í§àÊŒ¹ÁÑ¸Â°Ò¹¢Í§ÊÒÁàËÅÕèÂÁ¹Õè·ÕèÅÒ¡¨Ò¡ Ø´ A 5. ¶ŒÒ D(0, 2) à»š¹ Ø´¡Öè§¡ÅÒ§ÃÐËÇ‹Ò§ Ø´ A(-2, 1) áÅÐ C(x, y) áÅÐ¶ŒÒ C(x, y) à»š¹

Ø´¡Öè§¡ÅÒ§ÃÐËÇ‹Ò§ Ø´ A áÅÐ B(x1, y1) áÅŒÇ¨§ËÒ x1 + y1


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6. ¶ŒÒ O(x, 3) à»š¹ Ø´ÈÙ¹Â�¡ÅÒ§¢Í§Ç§¡ÅÁÇ§Ë¹Öè§«Öè§ÁÕ Ø´ A(-2, 0) áÅÐ B(5, 7) ÍÂÙ‹º¹àÊŒ¹ÃÍºÇ§¡ÅÁ¢Í§Ç§¡ÅÁ¹Õé ¨§ËÒ x

7. ¡íÒË¹´ A(-3, 5), B(4, 6) áÅÐ C(5, 5) à»š¹ Ø´ÂÍ´ÁØÁ¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ ABC «Öè§

ºÃÃ ØÍÂÙ‹ã¹Ç§¡ÅÁ·ÕèÁÕ Ø´ÈÙ¹Â�¡ÅÒ§ÍÂÙ‹·Õè Ø´ (x, y) ¨§ËÒ Ø´ (x, y)


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8. ¡íÒË¹´ A(6, 7), B(1, 2) áÅÐ C(11, 2) à»š¹ Ø´ÂÍ´¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ ABC ¨§¾×é¹·Õè¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ ABC

9. ¡íÒË¹´ A(-2, 4), B(-2, -2) áÅÐ C(6, -2) à»š¹ Ø´ÂÍ´¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ ABC ¨§

ËÒ Ø´ÈÙ¹Â�¡ÅÒ§áÅÐÃÑÈÁÕ¢Í§Ç§¡ÅÁ·ÕèÅŒÍÁÃÍºÃÙ»ÊÒÁàËÅÕèÂÁ ABC 10. ¶ŒÒ A(3, 8), B(1, 1) áÅÐ C(7, 5) à»š¹ Ø´ÂÍ´ÁØÁ¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ ABC ¨§ËÒ¤ÇÒÁ

ÂÒÇ¢Í§àÊŒ¹ÁÑ¸Â°Ò¹·ÕèÅÒ¡¨Ò¡ÁØÁ A ÁÒÂÑ§´ŒÒ¹ BC


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áºº½ƒ¡ËÑ ·Õè 3 (¤ÇÒÁªÑ¹¢Í§àÊŒ¹µÃ§) 1. ¨§ËÒ¤ÇÒÁªÑ¹¢Í§àÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´µ‹Íä»¹Õé

1.1. (0, 0) áÅÐ (3, 4)

1.2. (0, 0) áÅÐ (-5, -6)

1.3. (1, 2) áÅÐ (3, 4)

1.4. (-2, 3) áÅÐ (-4, 5)

1.5. (-3, -4) áÅÐ (5, 6)

2. ¡íÒË¹´ A(-2, -2), V(4, -2), C(x, y) áÅÐ D(-2, 2) à»š¹ Ø´ÂÍ´ÁØÁ¢Í§ÃÙ»

ÊÕèàËÅÕèÂÁ¤Ò§ËÁÙ â´ÂÁÕ AB à»š¹°Ò¹«Öè§ÂÒÇà»š¹ÊÍ§à·‹Ò¢Í§¤ÇÒÁÂÒÇ CD ¨§ËÒ¤ÇÒÁªÑ¹¢Í§ BC


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3. ¨§áÊ´§Ç‹ÒàÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (1, 2) áÅÐ (4, 6) ¢¹Ò¹¡ÑºàÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (-3, 4) áÅÐ (0, 8)

4. ¶ŒÒàÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (-3, -5) áÅÐ (k, -4) ¢¹Ò¹¡ÑºàÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (4, 3)

áÅÐ (6, 4) ¨§ËÒ¤‹Ò k

5. ¡íÒË¹´ A(5, 6), B(-1, 2) áÅÐ C(7, 0) à»š¹ Ø´ÂÍ´¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ ABC ¶ŒÒ D

áÅÐ E à»š¹ Ø´¡Öè§¡ÅÒ§¢Í§´ŒÒ¹ AB áÅÐ AC ¨§áÊ´§Ç‹Ò DE ¢¹Ò¹¡Ñº BC áÅÐ DE =1

2BC


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6. ¡íÒË¹´ A(-3, -1), B(5 ,3), C(3, 5) áÅÐ D(1, 7) à»š¹ Ø´ÂÍ´¢Í§ÃÙ»ÊÕèàËÅÕèÂÁABCD ¶ŒÒ P,Q,R áÅÐ S à»š¹ Ø´¡Öè§¡ÅÒ§¢Í§´ŒÒ¹ AB, BC, CD áÅÐ DA µÒÁÅíÒ´Ñº ¨§áÊ´§Ç‹Ò PQRS à»š¹ÊÕèàËÅÕèÂÁ´ŒÒ¹¢¹Ò¹

7. ¶ŒÒ Ø´ (a, 1), (2, 3) áÅÐ (4, 7) ÍÂÙ‹º¹àÊŒ¹µÃ§à´ÕÂÇ¡Ñ¹ ¨§ËÒ¤‹Ò a

8. ¨§áÊ´§Ç‹Ò A(-2, 3), B(4, 5), C(2,9) áÅÐ D(-1, 8) à»š¹ Ø´ÂÍ´ÁØÁ¢Í§ÃÙ»ÊÕèàËÅÕèÂÁ

¤Ò§ËÁÙ


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9. ¨§áÊ´§Ç‹ÒÊ‹Ç¹¢Í§àÊŒ¹µÃ§·ÕèÅÒ¡àª×èÍÁ Ø´¡Öè§¡ÅÒ§¢Í§´ŒÒ¹ 2 ´ŒÒ¹ ¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁã´æ Â‹ÍÁ¢¹Ò¹áÅÐÂÒÇà»š¹¤ÃÖè§Ë¹Öè§¢Í§´ŒÒ¹·ÕèàËÅ×Í

10. §áÊ´§Ç‹ÒÊ‹Ç¹¢Í§àÊŒ¹µÃ§·ÕèÅÒ¡àª×èÍÁ Ø´¡Öè§¡ÅÒ§¢Í§´ŒÒ¹·ÕèäÁ‹¢¹Ò¹¡Ñ¹¢Í§ÃÙ»ÊÕèàËÅÕèÂÁ¤Ò§ËÁÙÂ‹ÍÁ

¢¹Ò¹¡Ñº´ŒÒ¹¤Ù‹¢¹Ò¹

11. ¨§ËÒ¤ÇÒÁªÑ¹¢Í§àÊŒ¹µÃ§·ÕèÅÒ¡ÁÒµÑé§©Ò¡¡ÑºàÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (-2, 3) áÅÐ (4, -5)


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12. §áÊ´§Ç‹ÒàÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (1, 3) áÅÐ (6, 5) µÑé§©Ò¡¡ÑºàÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (-1 ,-3) áÅÐ (-3, 2)

13. ¶ŒÒàÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (4, 1) áÅÐ (1, 4) µÑé§©Ò¡¡ÑºàÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (m, 5) áÅÐ

(-2, 6) áÅŒÇ¨§ËÒ¤‹Ò m

14. §áÊ´§Ç‹ÒàÊŒ¹·áÂ§ÁØÁ¢Í§ÃÙ»ÊÕèàËÅÕèÂÁ ÑµØÃÑÊÂ‹ÍÁµÑé§©Ò¡¡Ñ¹


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15. ¨§áÊ´§Ç‹Ò¶ŒÒàÊŒ¹ÁÑ¸Â°Ò¹¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁÂÒÇà·‹Ò¡Ñ¹ÊÍ§àÊŒ¹áÅŒÇ ÃÙ»ÊÒÁàËÅÕèÂÁ¹Ñé¹¨Ðà»š¹ÊÒÁàËÅÕèÂÁË¹ŒÒ ÑèÇ

16. àÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´¡Öè§¡ÅÒ§¢Í§Ê‹Ç¹¢Í§àÊŒ¹µÃ§·Õèàª×èÍÁ Ø´ (1, 2) áÅÐ (3, 4) áÅÐ¢¹Ò¹¡Ñº

àÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (-5, 4) áÅÐ (-3, 5) ÁÕÊÁ¡ÒÃàÊŒ¹µÃ§à·‹Ò¡Ñºà·‹Òã´


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17. ¡íÒË¹´ ABC à»š¹ÃÙ»ÊÒÁàËÅÕèÂÁË¹ŒÒ ÑèÇ â´ÂÁÕ BC à»š¹°Ò¹ ¶ŒÒ¾Ô¡Ñ´¢Í§ Ø´ B áÅÐ C ¤×Í (1, 9) áÅÐ (5, 1) ¨§ËÒÊÁ¡ÒÃàÊŒ¹µÃ§·Õèà»š¹Ê‹Ç¹ÊÙ§¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁÃÙ»¹Õé

18. ¡íÒË¹´ A(-2, -1), B(5, -7) áÅÐ C(-3, 4) à»š¹ Ø´ÂÍ´ÁØÁ¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ ABC

¨§ËÒÊÁ¡ÒÃàÊŒ¹µÃ§·Õèà»š¹Ê‹Ç¹ÊÙ§¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁÃÙ»¹Õé


16

áºº½ƒ¡ËÑ ·Õè 4 (ÊÁ¡ÒÃ¢Í§¡ÃÒ¿àÊŒ¹µÃ§) 1. ¨§ºÍ¡¤ÇÒÁªÑ¹áÅÐ Ø´·ÕèàÊŒ¹µÃ§µ‹Íä»¹ÕéµÑ´á¡¹ x áÅÐ á¡¹ y

1) y= -45

¤ÇÒÁªÑ¹ = µÑ´á¡¹ x ·Õè Ø´ µÑ´á¡¹ y ·Õè Ø´

2) x= -5 ¤ÇÒÁªÑ¹ = µÑ´á¡¹ x ·Õè Ø´ µÑ´á¡¹ y ·Õè Ø´

3) x5+

y

3 = 1

¤ÇÒÁªÑ¹ = µÑ´á¡¹ x ·Õè Ø´ µÑ´á¡¹ y ·Õè Ø´

2. ¶ŒÒàÊŒ¹µÃ§ ax +10y = 6 ¢¹Ò¹¡ÑºàÊŒ¹µÃ§ x+2y = 8 ¨§ËÒ¤‹Ò a

3. ¶ŒÒàÊŒ¹µÃ§ 3x+by = 5 µÑé§©Ò¡¡ÑºàÊŒ¹µÃ§ 5x+3y-10 = 0 ¨§ËÒ¤‹Ò b


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4. ¨§ËÒÊÁ¡ÒÃ¢Í§àÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (1, 2) áÅÐ (4, 3)

5. ¨§ËÒÊÁ¡ÒÃ¢Í§àÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (3, -4) áÅÐ (5, -6)

6. ¨§ËÒÊÁ¡ÒÃ¢Í§àÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (3, 4) áÅÐÁÕ¤ÇÒÁªÑ¹à·‹Ò¡Ñº 3

4

7. ¨§ËÒÊÁ¡ÒÃ¢Í§àÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (-1, -2) áÅÐ¢¹Ò¹¡ÑºàÊŒ¹µÃ§ 2x-3y+4 = 0


18

8. ¨§ËÒÊÁ¡ÒÃ¢Í§àÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (-2, 3) áÅÐ¢¹Ò¹¡ÑºàÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (-2, 8) áÅÐ (1, 9)

9. ¨§ËÒÊÁ¡ÒÃ¢Í§àÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (1, 4) áÅÐµÑé§©Ò¡¡ÑºàÊŒ¹µÃ§ 3x+4y+5 = 0

10. §ËÒÊÁ¡ÒÃ¢Í§àÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (-4, -5) áÅÐµÑé§©Ò¡¡ÑºàÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (1, 2) áÅÐ (6, 5)


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11. ¨§ËÒÊÁ¡ÒÃ¢Í§àÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´µÑ´¢Í§àÊŒ¹µÃ§ x+y = 5 áÅÐ x-y = 1 áÅÐ¢¹Ò¹¡ÑºàÊŒ¹µÃ§ 4x-5y+6 = 0

12. §ËÒÊÁ¡ÒÃàÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´µÑ´¢Í§àÊŒ¹µÃ§ x+2y = 3 áÅÐ 3y-x = 2 áÅÐµÑé§©Ò¡¡ÑºàÊŒ¹µÃ§ 5x-2y+6 = 0

13. ¡íÒË¹´ A(-1, 9), B(-2, 1) áÅÐ C(5, 6) à»š¹ Ø´ÂÍ´ÁØÁ¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ ABC ¨§ËÒÊÁ¡ÒÃàÊŒ¹µÃ§«Öè§à»š¹Ê‹Ç¹ÊÙ§¢Í§ÊÒÁàËÅÕèÂÁÃÙ»¹Õé·ÕèÅÒ¡¨Ò¡ Ø´ A


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14. ¡íÒË¹´ A(2, 5), B(-2, -2) áÅÐ C(4, 0) à»š¹ Ø´ÂÍ´¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ ABC ¨§ËÒÊÁ¡ÒÃ¢Í§àÊŒ¹ÁÑ¸Â°Ò¹¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ¹Õé·ÕèÅÒ¡¨Ò¡ Ø´ÂÍ´ÁØÁ A

15. ¨§ËÒÊÁ¡ÒÃàÊŒ¹µÃ§·ÕèÁÕÃÐÂÐË‹Ò§¨Ò¡ Ø´ (1, 2) áÅÐ (6, 4) à»š¹ÃÐÂÐà·‹Ò¡Ñ¹


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áºº½ƒ¡ËÑ ·Õè 5 (ÃÐÂÐË‹Ò§ÃÐËÇ‹Ò§àÊŒ¹µÃ§¡Ñº¨Ø áÅÐÃÐÂÐÃÐËÇ‹Ò§àÊŒ¹¤Ù‹¢¹Ò¹) 1. ¨§ËÒÃÐÂÐÃÐËÇ‹Ò§àÊŒ¹µÃ§¡Ñº Ø´·Õè¡íÒË¹´ãËŒµ‹Íä»¹Õé

1.1. 3x+4y+5 = 0 ¡Ñº Ø´ (3, 4)

1.2. 4x-3y-8 = 0 ¡Ñº Ø´ (1, 2)

1.3. 6x+8y+12 = 0 ¡Ñº Ø´ (1, -1) 2. ¨§ËÒÃÐÂÐË‹Ò§ÃÐËÇ‹Ò§àÊŒ¹¤Ù‹¢¹Ò¹µ‹Íä»¹Õé

2.1. 3x+4y-5 = 0 ¡Ñº 3x+4y-10 = 0

2.2. 4x-3y-10 = 0 áÅÐ 8x-6y+10 = 0

2.3. 12x+5y = 17 ¡Ñº y = -125x -

9

5


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3. ¨§ËÒÊÁ¡ÒÃàÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (2, 1) áÅÐÍÂÙ‹Ë‹Ò§¨Ò¡ Ø´¡íÒà¹Ô´à»š¹ÃÐÂÐ 2 Ë¹‹ÇÂ 4. ¶ŒÒàÊŒ¹µÃ§ 3x+4y-24=0 µÑ´á¡¹ x ·Õè Ø´ A áÅÐ Ñ´á¡¹ y ·Õè Ø´ B ¨§ËÒ Ø´ÈÙ¹Â�¡ÅÒ§

¢Í§Ç§¡ÅÁ·ÕèÅŒÍÁÃÙ»ÊÒÁàËÅÕèÂÁ OAB àÁ×èÍ O à»š¹ Ø´¡íÒà¹Ô´ 5. ¨§ËÒÊÁ¡ÒÃàÊŒ¹µÃ§«Öè§µÑé§©Ò¡¡ÑºàÊŒ¹µÃ§ 12y=5x-7 áÅÐÍÂÙ‹Ë‹Ò§¨Ò¡ Ø´ (-1, 2) à»š¹ÃÐÂÐ

à·‹Ò¡Ñº 3 Ë¹‹ÇÂ


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6. ¶ŒÒàÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ (-5, 4) µÑ´á¡¹ x áÅÐá¡¹ y ·Õè Ø´ (a, 0) áÅÐ (0, b) µÒÁÅíÒ´ÑºáÅÐ ab=10 ¶ŒÒ (a, b) ÍÂÙ‹ã¹¤ÇÍ´ÃÑ¹µ�·Õè 1 ¨§ËÒ a+b

7. ¶ŒÒàÊŒ¹µÃ§ 4x-3y+10 = 0 áº‹§¤ÃÖè§áÅÐµÑé§©Ò¡¡ÑºÊ‹Ç¹¢Í§àÊŒ¹µÃ§ AB ¶ŒÒ A ÁÕ¾Ô¡Ñ´ (-

4, 3) ¨§ËÒ¾Ô¡Ñ´¢Í§ Ø´ B


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8. ¶ŒÒ D(1, 5), E(2, 3) áÅÐ F(4, 6) à»š¹ Ø´¡Öè§¡ÅÒ§¢Í§´ŒÒ¹ AB, BC áÅÐ CA µÒÁÅíÒ´Ñº¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ ABC ¨§ÊÁ¡ÒÃàÊŒ¹µÃ§·ÕèÅÒ¡¼‹Ò¹ Ø´ A áÅÐ¢¹Ò¹¡Ñº´ŒÒ¹ BC


25

9. ¶ŒÒ A(4, 6), B(-6, 1) áÅÐ C(-2, 2) à»š¹ Ø´ÂÍ´ÁØÁ¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ ABC ¶ŒÒ¡íÒË¹´ãËŒ BC à»š¹´ŒÒ¹°Ò¹ áÅÐ A à»š¹ÁØÁÂÍ´¢Í§ÊÒÁàËÅÕèÂÁ¹Õé ¨§ËÒ¾×é¹·Õè¢Í§ÃÙ»ÊÒÁàËÅÕèÂÁ ABC ¹Õé

10. àÊŒ¹µÃ§ l1 ÅÒ¡¼‹Ò¹ Ø (2, 2) µÑ´á¡¹ x áÅÐá¡¹ y ·Ò§ºÇ¡ ·íÒãËŒ¼ÅºÇ¡¢Í§ÃÐÂÐµÑ´

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เรขาคณิตวิเคราะห์ · 2017-03-18 ·...

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