The document discusses key concepts relating to slope and lines including: - Two lines are parallel if they have the same slope - Two lines are perpendicular if their slopes are the negative inverse of each other - It provides an example of finding the value of a given four points and asks to determine a such that the lines are perpendicular - For a second problem, it asks to find the coordinates of the fourth vertex D of a parallelogram given vertices A, B, and C.

1. The Slope (Gradient)

2. The Slope (Gradient)

3. The Slope (Gradient) y x

4. The Slope (Gradient) l y x

5. The Slope (Gradient) l y x

6. The Slope (Gradient) l y x

7. The Slope (Gradient) l y x

8. The Slope (Gradient) l L y x

9. The Slope (Gradient) l L y x

10. The Slope (Gradient) l L y x

11. The Slope (Gradient) l L y x

12. The Slope (Gradient) l L y x

13. The Slope (Gradient) l L y x

14. The Slope (Gradient) l L y x

15. The Slope (Gradient) l L y x

16. The Slope (Gradient) l L y x

17. The Slope (Gradient) l L y x

18. Two lines are parallel iff they have the same slope

19. Two lines are parallel iff they have the same slope Two lines are perpendicular iff their slopes are the negative inverse of each other

20. Two lines are parallel iff they have the same slope Two lines are perpendicular iff their slopes are the negative inverse of each other

21. Two lines are parallel iff they have the same slope Two lines are perpendicular iff their slopes are the negative inverse of each other e.g. A , B , C and D are the points (1,1), (2,3), (3,2) and ( a ,4) Find a such that;

22. Two lines are parallel iff they have the same slope Two lines are perpendicular iff their slopes are the negative inverse of each other e.g. A , B , C and D are the points (1,1), (2,3), (3,2) and ( a ,4) Find a such that;

23. Two lines are parallel iff they have the same slope Two lines are perpendicular iff their slopes are the negative inverse of each other e.g. A , B , C and D are the points (1,1), (2,3), (3,2) and ( a ,4) Find a such that;

24. Two lines are parallel iff they have the same slope Two lines are perpendicular iff their slopes are the negative inverse of each other e.g. A , B , C and D are the points (1,1), (2,3), (3,2) and ( a ,4) Find a such that;

25. Two lines are parallel iff they have the same slope Two lines are perpendicular iff their slopes are the negative inverse of each other e.g. A , B , C and D are the points (1,1), (2,3), (3,2) and ( a ,4) Find a such that;

26. Two lines are parallel iff they have the same slope Two lines are perpendicular iff their slopes are the negative inverse of each other e.g. A , B , C and D are the points (1,1), (2,3), (3,2) and ( a ,4) Find a such that;

27. Two lines are parallel iff they have the same slope Two lines are perpendicular iff their slopes are the negative inverse of each other e.g. A , B , C and D are the points (1,1), (2,3), (3,2) and ( a ,4) Find a such that;

28. Two lines are parallel iff they have the same slope Two lines are perpendicular iff their slopes are the negative inverse of each other e.g. A , B , C and D are the points (1,1), (2,3), (3,2) and ( a ,4) Find a such that;

29. Two lines are parallel iff they have the same slope Two lines are perpendicular iff their slopes are the negative inverse of each other e.g. A , B , C and D are the points (1,1), (2,3), (3,2) and ( a ,4) Find a such that;

30. Two lines are parallel iff they have the same slope Two lines are perpendicular iff their slopes are the negative inverse of each other e.g. A , B , C and D are the points (1,1), (2,3), (3,2) and ( a ,4) Find a such that;

31. Two lines are parallel iff they have the same slope Two lines are perpendicular iff their slopes are the negative inverse of each other e.g. A , B , C and D are the points (1,1), (2,3), (3,2) and ( a ,4) Find a such that;

32. (ii) A (4,0), B (1,5) and C (–3,–5) are three vertices of a parallelogram ABCD . Find the coordinates of D , the fourth vertex of the parallelogram.

33. (ii) A (4,0), B (1,5) and C (–3,–5) are three vertices of a parallelogram ABCD . Find the coordinates of D , the fourth vertex of the parallelogram. y x

34. (ii) A (4,0), B (1,5) and C (–3,–5) are three vertices of a parallelogram ABCD . Find the coordinates of D , the fourth vertex of the parallelogram. 3 5 y x

35. (ii) A (4,0), B (1,5) and C (–3,–5) are three vertices of a parallelogram ABCD . Find the coordinates of D , the fourth vertex of the parallelogram. 3 5 3 5 y x

36. (ii) A (4,0), B (1,5) and C (–3,–5) are three vertices of a parallelogram ABCD . Find the coordinates of D , the fourth vertex of the parallelogram. 3 5 3 5 y x

37. (ii) A (4,0), B (1,5) and C (–3,–5) are three vertices of a parallelogram ABCD . Find the coordinates of D , the fourth vertex of the parallelogram. 3 5 3 5 y x

38. To prove three points ( A , B , C) are collinear;

39. To prove three points ( A , B , C) are collinear;

40. To prove three points ( A , B , C) are collinear;

41. To prove three points ( A , B , C) are collinear;

42. To prove three points ( A , B , C) are collinear; Exercise 5B; 2ace, 3bd, 4 ii, iv , 5ae, 8, 9a, 11ac, 13, 15, 18, 19, 20, 24*