1. COORDINATE GEOMETRY Week commencing Monday 16 th November 2009 Learning Intention: To be able to determine if two lines are parallel or perpendicular. Contents: 1.Parallel and Perpendicular LinesParallel and Perpendicular Lines 2.ExamplesExamples 3.Assignment 4Assignment 4

2. COORDINATE GEOMETRY PARALLEL AND PERPENDICULAR LINES Parallel Lines have the same gradient. Perpendicular Lines are at right angles to each other.

3. COORDINATE GEOMETRY PARALLEL AND PERPENDICULAR LINES Parallel Two lines y = m 1 x + c 1 and y = m 2 x + c 2 are parallel if m 1 = m 2. Perpendicular If m 1 x m 2 = -1 then the two lines y = m 1 x + c 1 and y = m 2 x + c 2 are perpendicular. Therefore, if the gradient of line 1 = m, then the gradient of line 2 = -1/m

4. COORDINATE GEOMETRY EQUATION OF A LINE GIVEN TWO POINTS Examples: Work out the gradient of the line that is perpendicular to the lines with these gradients: (i) 3(ii)-4(iii)-½ Solutions: (i)m = 3therefore perpendicular m = -1/3 (ii)m = -4therefore perpendicular m = -1/-4 = 1/4 (iii)m = -½ therefore perpendicular m = -1/-½ = 2

5. COORDINATE GEOMETRY EQUATION OF A LINE GIVEN TWO POINTS Example: Determine whether the lines y – 3x + 3 = 0 and 3y + x = 6 are parallel, perpendicular or neither. Solution: To compare the two lines we need to know the gradients of the two lines. Line 1: y – 3x + 3 = 0rewrite in form y = mx + c y = 3x – 3so m = 3 Line 2:3y + x = 6rewrite in form y = mx + c 3y = -x + 6 y = -1/3x + 6so m =-1/3 Comparing gradients: 3 x -1/3 = -1, so lines are perpendicular

6. COORDINATE GEOMETRY EQUATION OF A LINE GIVEN TWO POINTS Example: Line L is perpendicular to the line 2y – x + 3 = 0 at the point (4, ½). Determine the equation of the line L. Solution: To find the equation of a line we need a point and a gradient. We have a point and can find the gradient by first finding the gradient of the given line. 2y – x + 3 = 0rewrite in form y = mx + c 2y = x – 3 y = ½x – 3/2m = ½ Therefore perpendicular gradient = -2 Substitute into formula for equation of a line to get: y – ½ = -2(x – 4) y – ½ = -2x + 8 y = -2x + 8 + ½ = -2x + 17/2

7. COORDINATE GEOMETRY Assignment 4 Follow the link for Assignment 4 in Moodle Course Area underneath Coordinate Geometry. Assignments to be completed by 5:00pm on Monday 23 rd November 2009.