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

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

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

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

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