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

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

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

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)

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

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

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

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

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

3) Classify ΔDEF as scalene, isosceles or equilateral

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)

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

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

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

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

Determine the slope of each line. 1) 2)

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

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

Be careful when writing the formula…

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

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

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

Horizontal Lines: Vertical Lines:

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

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.

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

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

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

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

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

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