1. COORDINATE GEOMETRY Week commencing Monday 9th November 2009
Learning Intention:
Given two points on a line to be able to find the equation of the line.
Contents:
1. Equation of a line given two points
2. Examples
3. Assignment 3 1

2. EQUATION OF A LINE GIVEN TWO POINTS
COORDINATE GEOMETRY
EQUATION OF A LINE GIVEN TWO POINTS
If given the two points on a line, (x1, y1) and (x2, y2), we can find the equation of line using the formula: 2

3. EQUATION OF A LINE GIVEN TWO POINTS
COORDINATE GEOMETRY
EQUATION OF A LINE GIVEN TWO POINTS
Example:
The find the equation of the line that passes through the points (1, 2) and (5, 4).
Solution:
(x1, y1) = (1, 2) (x2, y2) = (5, 4)
Substituting into the formula we get: 3

4. EQUATION OF A LINE GIVEN TWO POINTS
COORDINATE GEOMETRY
EQUATION OF A LINE GIVEN TWO POINTS
Example:
The lines y = 4x – 7 and 2x + 3y -21 = 0 intersect at the point A. The point B has coordinates (-2, 8). Find the equation of the line that passes through the points A and B. Write your answer in the form ax + by + c = 0.
Solution:
We now have two points: (3, 5) and (-2, 8)
We can use these two points to find the equation of the line:
First step is to find the point A. We find the point where the two lines intersect by solving the equations simultaneously.
y = 4x – 7 (1) 2x + 3y – 21 = 0 (2)
Substitute equation (1) into (2) to get:
2x + 3(4x – 7) -21 = 0
2x + 12x – 21 – 21 = 0
14x = 42
x = 3 y = 4(3) – 7 = 12 – 7 = 5
Coordinates of A are (3, 5) 4

5. COORDINATE GEOMETRY Assignment 3
The assignment this week is a collaborative task. There are 6 questions in the discussion forum for Assignment 3.
Each student must take one question and post their solution under the relevant thread in the discussion forum.
A maximum of 3 solutions per question so if there are already 3 solutions posted to the question you have chosen you must choose another question. 5