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Analytical geometry and the straight line

Chapter 29. Analytical geometry and the straight line. Some important concepts:. These are called straight line equations. eg. 1.

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Analytical geometry and the straight line

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  1. Chapter 29 Analytical geometry and the straight line FYHS-Kulai by Chtan

  2. Some important concepts: These are called straight line equations. FYHS-Kulai by Chtan

  3. eg. 1 A line is parallel with 2x+3y=4 and it cuts the axes at A and B. Given the area of the triangle OAB is 3 units squares, where O is the origin. Find the equation of the straight line. FYHS-Kulai by Chtan

  4. eg. 2 FYHS-Kulai by Chtan

  5. FYHS-Kulai by Chtan

  6. The straight line passing through the point (h,k) and having a gradient m can be written as : FYHS-Kulai by Chtan

  7. eg. 3 The straight line AB has an equation y+2x+8=0. AB intersects the x-axis at point A and intersects the y-axis at point B. Point P lies on AB such that AP:PB = 1:3. Find(a) the coordinates of P(b) the equation of the straight line that passes through P and perpendicular to AB. FYHS-Kulai by Chtan

  8. The angle Ө between two straight lines with gradients : FYHS-Kulai by Chtan

  9. eg. 4 FYHS-Kulai by Chtan

  10. The length of the perpendicular from the point (h,k) to the straight line Note : the sign is chosen in order to make the perpendicular from the origin positive. FYHS-Kulai by Chtan

  11. eg. 5 FYHS-Kulai by Chtan

  12. The equations of the bisectors of the angle between 2 straight lines : FYHS-Kulai by Chtan

  13. Internal division FYHS-Kulai by Chtan

  14. External division FYHS-Kulai by Chtan

  15. Z is the mid-point of BC A G divides ZA in the ratio 1:2 G C Z B G is one third the way up the median from A. FYHS-Kulai by Chtan

  16. How to find the distance between these 2 lines ? FYHS-Kulai by Chtan

  17. Two perpendicular straight lines FYHS-Kulai by Chtan

  18. Equation of a straight lines passing through the point of intersection of two given straight lines. All straight lines passing through the point of intersection of two lines : a’x+b’y+c’=0 and a”x+b”y+c”=0 are given by the equation : a’x+b’y+c’ + λ(a”x+b”y+c”)=0 where λ is any constant. FYHS-Kulai by Chtan

  19. Circumcircle of a triangle外接圆 Note : intersection of the bisector of the lines is the centre of the circle. FYHS-Kulai by Chtan

  20. Incircle of a triangle内切圆 Note : intersection point of angle-of-bisector lines is the centre of the circle. FYHS-Kulai by Chtan

  21. Miscellaneous Examples FYHS-Kulai by Chtan

  22. eg. 6 PN, the perpendicular from P(3,4) to the line 2x+3y=1 is produced to Q such that NQ=PN. Find the coordinates of Q. FYHS-Kulai by Chtan

  23. eg. 7 Determine whether the points (3,-2), (-1,7) are on the same or opposite sides of the line 2x-5y=13. FYHS-Kulai by Chtan

  24. eg. 8 ABCD is a square; A is the point (0,-2) and C the point (5,1), AC being a diagonal. Find the coordinates of B and D. FYHS-Kulai by Chtan

  25. eg. 9 Find the acute angle between the two lines 2y-x=3, 3y+4x=5. FYHS-Kulai by Chtan

  26. eg. 10 Find the distance of the point (-2,1) from the line 2y-x-7=0 FYHS-Kulai by Chtan

  27. eg. 11 Find the equations of the lines bisecting the angles between the lines y=3x, y=x+2. Verify that the bisectors are perpendicular. FYHS-Kulai by Chtan

  28. eg. 12 Find the equations of the straight lines drawn through the point (1,-2) making angles of 45° with the x-axis. FYHS-Kulai by Chtan

  29. eg. 13 Find the ratio in which the line 4x-y=3 divides the line joining the points (2,-1), (-3,2). FYHS-Kulai by Chtan

  30. eg. 14 Prove that the lines 7x+2y=5, 6x+3y=5, 5x+4y=5 are concurrent. FYHS-Kulai by Chtan

  31. eg. 15 Find the equation of the straight line joining the point of intersection of the lines 4x-y=7, 2x+3y=1 to the origin. FYHS-Kulai by Chtan

  32. No need to do Ex 10b Q1, 2, 3, 4, 12 Misc Ex 10 FYHS-Kulai by Chtan

  33. The end FYHS-Kulai by Chtan

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