1. Material Taken From: Mathematics for the international student Mathematical Studies SL Mal Coad, Glen Whiffen, John Owen, Robert Haese, Sandra Haese and Mark Bruce Haese and Haese Publications, 2004

2. Horizontal x-axis vertical y-axis origin Cartesian Coordinate Plane Section A - Distance Between Two Points

3. Every point on the graph will be represented with two numbers written in parenthesis. (4, -3) x - axis y- axis

4. x - axis y - axis The first number is the x-coordinate and tells you how far to go left or right. The second number is the y-coordinate and tells you how far to go up or down. (4, -3)

5. x - axis y - axis I II III IV The axes divide the graph into 4 quadrants. Each quadrant has a number. ( +, +)( -, +) ( -, -)( +, -)

6. Plot:(-3, 5)(-4, -2) (4, 3)(3, -4)

8. Distance Formula The distance between points A(x 1, y 1 ) and B(x 2, y 2 ) is defined as: d =

9. 1) Find the distance between (2, -4) and (-5, -1)

10. 2) Find the distance between (-2, 5) and (3, -1)

11. 3) Classify ΔDEF as scalene, isosceles or equilateral

12. 4) Use the distance formula to show that triangle ABC is right angled if A is (3, -4), B is (-2, -5) and C is (1, 6)

13. 5) Find b given that A(3, b) and B(-1, 2) are units apart.

14. Slope/Gradient Slope of a line is the __________, of the line. steepness Section B - Gradient

15. Slope Slope can be ________, ________, or ______. It is also possible for slope to ___________. zeropositive negative not exist

16. Slope To determine slope you need to know how far the line ______ and how far the line ______. “runs” “rises” slope = m =

17. Determine the slope of each line. 1) 2)

18. 3) Through (-2, 1) draw a line with gradient

19. Slope of a Line x1x1 x2x2 x 2 - x 1 m = =

20. Be careful when writing the formula…

21. 4) Find the slope of the line through the points (1, 6) and (3, -2).

22. 5) Find the slope of the line through the points (7, -6) and (-5, 2).

23. (-1, 2) and ( 2, 2) (3, 4) and (3, 1) Consider:

24. Horizontal Lines: Vertical Lines:

25. A line with a positive slope (m> 0)____ from left to right A line with a negative slope (m< 0) ____ from left to right A line with zero slope (m = 0) is ________ A line with undefined slope is _______ The Slope of a Line rises falls horizontal vertical a b d f c e

26. Parallel & Perpendicular Lines Two lines are parallel if and only if they have the same slope. Two lines are perpendicular if and only if their slopes are opposite reciprocals.

27. 6) If a line has gradient find the gradient of all lines a)parallel to the given line b)perpendicular to the given line

28. 7) Find a given that the line joining M(3, a) and N(a, 5) has a gradient of

29. 8) Find t given that the line joining A(-1, -3) to B(4, t) is perpendicular to a line with gradient

30. Collinear Three or more points are collinear if they line on the same straight line.

31. 9) Determine whether or not the set of points A(0, -2), B(-1, -5) and C(4, 10) are collinear.

32. Homework Exercise 7A.2, pg206 – #1aceg, #2ce, #3a, #4a Exercise 7B.1, pg209 – #2abd Exercise 7B.2, pg209 – #1adg, #4a Exercise 7B.3, pg211 – #1df, #2, #3a, #4a, #5c, #6, #7