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 AND Mathematical Studies Standard Level Peter Blythe, Jim Fensom, Jane Forrest and Paula Waldman de Tokman Oxford University Press, 2012

2. horizontal x-axis vertical y-axis origin Cartesian Coordinate Plane

3. Every point on the graph will be represented with two numbers written in parenthesis. (4, -3) 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. x - axis y - axis I II III IV The axes divide the graph into 4 quadrants. Each quadrant has a number. ( +, +)( -, +) ( -, -)( +, -)

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

6. Rules of Pythagoras Right Triangles: One of its angles must be a right angle (90°). The side opposite of the right angle is called the hypotenuse. The other sides of the triangle are called the legs. All Triangles: The sum of the three angles equals 180°. hypotenuse leg 1 leg 2

7. Pythagorean Theorem c a b Only works in right triangles a 2 + b 2 = c 2

8. Find x: Practice

9. Distance Consider points: A (2, 2) B (8, 8) What is the distance of the line AB?

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

11. Find the distance between the following points: a) (2, -4) and (-5, -1) b) (0, 3) and (-6, 2) c) (-9, 12) and (7, 8) Practice

12. Midpoint Consider points: A (0, 2) B (8, 2) What is the midpoint of the line AB?

13. Midpoint Formula The midpoint M of the line segment joining A (x 1, y 1 ) and B (x 2, y 2 ) is:

14. Find the midpoint between the following points: a) (6, -2) and (2, -9) b) (-8, -4) and (5, -3) c) (9, 12) and (-1, 3) Practice

15. 12 cm 8 m 6 m 16 mm 7 mm In each of the figures find the: a) perimeter b) area