Co-ordinate geometry I

Co-ordinate geometry I

1. Co-ordinates are a means of describing the position of a point in relation to a fixed origin.

2. The gradient of a line

   • The slope of a line is measured by a gradient and the letter 'm' is often used to represent this
     • m=y2-y1/x2-x1
     • / positive gradient \ negative gradient - zero gradient | infinite gradient

3. Parallel and perpendicular lines

   • parallel lines --> m1=m2
     • perpendicular lines --> m1m2= -1

4. The distance between two points

   • You can use Pythagoras' theorem to find the distance between two points if you know their co-ordinates
     • length=√(x2-x1)*2 + (y2-y1)*2

5. The midpoint of a line joining two points

   • midpoint= ( (x1+x2)/2 , (y1+y2)/2 )

6. The equation of a straight line

   • y=mx+c

7. Drawing a line given its equation

   • There are several standard forms for the equation of a straight line.
     • x=a
       • All such lines are parallel to the y axis
     • y=b
       • All such lines are parallel to the x axis
     • y=mx
       • These are lines through the origin with the gradient m
     • y=mx+c
       • These lines have gradient m and a y intersect of c

8. Finding the equation of a line

   • y-y1 = m(x-x1)
   • y-y1/y2-y1 = x-x1/x2-x1
   • y-y1/x-x1 = y2-y1/x2-x1

9. The co-ordinates of the point of intersection of two lines are found by solving their equations simultaneously

10. The circle

    • A circle with centre (a,b), radius r has equation (x-a)*2 + (y-b)*2 = r*2
      • A circle with centre (0,0) has equation x*2 + y*2 = r*2