2. Coordinate Geometry m 1 = m 2 m 1 x m 2 = – 1 ax+by+c = 0 y = m x + c :intercept  -parallel -perpendicular :gradient  Gradient :general  Area Equation : Mid point Ratio theorem Distance

3. Coordinate Geometry Some extra vitamins 4u …

7. 6. Coordinate Geometry 6.2.2 Division of a Line Segment Q divides the line segment PR in the ratio PQ : QR = m : n n m P(x 1 , y 1 ) ‏ R(x 2 , y 2 ) ‏ Q(x, y) ‏ ● n m R(x 2 , y 2 ) ‏ P(x 1 , y 1 ) ‏ Q(x, y) ‏ Q(x, y) =

8. 6. Coordinate Geometry (Ratio Theorem) ‏ The point P divides the line segment joining the point M(3,7) and N(6,2) in the ratio 2 : 1. Find the coordinates of point P. P(x, y) = ● 1 2 N(6, 2) ‏ M(3, 7) ‏ P(x, y) ‏ = = P(x, y) =

9. 6. Coordinate Geometry m 1 .m 2 = –1 Perpendicular lines : P Q R S

10. 6. Coordinate Geometry (SPM 2006, P1, Q12) Diagram 5 shows the straight line AB which is perpendicular to the straight line CB at the point B . The equation of CB is y = 2x – 1 . Find the coordinates of B . [3 marks ] m CB = 2 m AB = – ½ Equation of AB is y = – ½ x + 4 At B, 2x – 1 = – ½ x + 4 x = 2, y = 3 So, B is the point (2, 3). x y O A(0, 4) ‏ C Diagram 5 B ● ● ● y = 2x – 1

11. 6. Coordinate Geometry Given points P(8,0) and Q(0,-6). Find the equation of the perpendicular bisector of PQ. m PQ = m AB = Midpoint of PQ = (4, -3) ‏ The equation : 4x + 3y -7 = 0 K1 K1 N1 or P Q x y O

12. TASK : To find the equation of the locus of the moving point P such that its distances from the points A and B are in the ratio m : n (Note : Sketch a diagram to help you using the distance formula correctly) 6 Coordinate Geometry

13. 6. Coordinate Geometry : the equation of locus Given that A(-1,-2) and B(2,1) are fixed points . Point P moves such that the ratio of AP to PB is 1 : 2. Find the equation of locus for P. 2 AP = PB x 2 + y 2 + 4x + 6y + 5 = 0 4 [ (x+1) 2 + (y+2) 2 ] = (x -2 ) 2 + (y -1) 2 3x 2 + 3y 2 + 12x + 18y + 15 = 0 F4 K1 J1 N1

14. Find the equation of the locus of the moving point P such that its distance from the point A(-2,3) is always 5 units. (≈ SPM 2005) ‏ ● 5 A(-2, 3) ‏ P(x, y) ‏ ● A(-2,3) ‏ Let P = (x, y) ‏ is the equation of locus of P.

15. Find the equation of the locus of point P which moves such that it is always equidistant from points A(-2, 3) and B(4, 9) . Constraint / Condition : PA = PB PA 2 = PB 2 (x+2) 2 + (y – 3) 2 = (x – 4) 2 + (y – 9) 2 x + y – 7 = 0 is the equation of locus of P. Note : This locus is actually the perpendicular bisector of AB A(-2, 3) ‏ ● B(4, 9) ‏ ● Locus of P ● P(x, y) ‏

16. Solutions to this question by scale drawing will not be accepted. (SPM 2006, P2, Q9) Diagram 3 shows the triangle AOB where O is the origin. Point C lies on the straight line AB . (a) Calculate the area, in units 2 , of triangle AOB . [2 marks ] (b) Given that AC : CB = 3 : 2, find the coordinates of C . [2 marks ] (c) A point P moves such that its distance from point A is always twice its distance from point B . (i) Find the equation of locus of P , (ii) Hence, determine whether or not this locus intercepts the y -axis. [6 marks ] x y O A(-3, 4) ‏ Diagram 3 C ● ● ● B(6, -2) ‏

17. (SPM 2006, P2, Q9) : ANSWERS 9(a) ‏ = 9 x y O A(-3, 4) ‏ Diagram 3 C ● ● ● B(6, -2) ‏ 3 2 9(b ) K1 N1 Use formula correctly N1 K1 Use formula To find area

18. (SPM 2006, P2, Q9) : ANSWERS √ AP = 2PB AP 2 = 4 PB 2 (x+3) 2 + (y – 4 ) 2 = 4 [(x – 6) 2 + (y + 2) 2 x 2 + y 2 – 18x + 8y + 45 = 0 N1 9(c) (i) ‏ K1 Use distance formula K1 Use AP = 2PB x y O A(-3, 4) ‏ C ● ● ● B(6, -2) ‏ 2 1 P(x, y) ‏ ● AP =

19. (SPM 2006, P2, Q9) : ANSWERS 9(c) (ii) x = 0, y 2 + 8y + 45 = 0 b 2 – 4ac = 8 2 – 4(1)(45) < 0 So, the locus does not intercept the y-axis. Use b 2 – 4ac K1 K1 Subst. x = 0 into his locus N1

20. Common errors… PA : PB = 2 : 3 then 2 PA = 3 PB

21. Actually, … PA : PB = 2 : 3 3 PA = 2 PB

22. More mistakes …… 3 2 PA 2 = 2 2 PB 2 9 PA 2 = 4 PB 2

23. Hear LOCUS Remember distance ! Rhombus .. The diagonals are perpendicular Rhombus, parallelogram, rectangle The diagonals share the same midpoint

24. TOPIC : Circular measures 2  –  A = ½ r 2 (  - sin  )  –    r r

30. To estimate median from Histogram 10 20 30 40 50 60 70 80 0.5 20.5 40.5 60.5 Age Frequency

31. Median from formula

38. Effects on changes to Data Unchanged x m x m x m  m  m  m Multiply by m +k +k +k Added by k Var  Int. Q range Med Mod Mean Measures of Dispersion Measures of Central Tendency Change of value  m 2

40. RECIPE OF SUCCESS ACHIEVE AIM ACT

41. Selamat Berjaya