1 / 33

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.

kenisha
Télécharger la présentation

Analytical geometry and the straight line

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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

More Related