Coordinate geometry

Coordinate geometry

1. y=mx+c

   • y= How far up
   • m= gradient
   • x= how far along
   • c= y-intercept (where it crosses the y-axis
   • ax+by+c=0
     • It can be rearranged from the for y=mx+c to make 0 the subject.

2. Parallel lines

   • A pair of lines are parallel if their gradient is equal
     • m1=m2
       • To work out the equation of a parallel line you use the equation y-y1=m(x-x1) given the gradient and the coordinate of the parallel line
         • e.g. A line is parallel to the line y+1/2x-5 and its intercept on the y-axis is (0,1). write down the equation of the line.
           • y-y1=m(x-x1) y-1=1/2(x-0) y-1=1/2x y=1/2x+1

3. ·

   • This equation is used to work out the gradient of a line, joining two coordinates
     • For example, work out the gradient of the line joining the points (2,3) and (5,7) m= (7-3)/(5-2). The gradient of the line is 4/3

4. You can find the equation of a line with the gradient m that passes through the point given a coordinate (x1,y1)

   • e.g. find the equation of the line with gradient 5 that passes through the point (3,2), The gradient is 5, so (y-2)/(x-3)=5. y-2=5(x-3). y-2=5x-15 y=5x-13

5. You can find the equation of the line that passes through two coordinates (x1,y1) and (x2,y2)

   • • For example, work out the gradient of the line that passes through the points (5,7) and (3,-1) and hence find the equation of the line. m=(-1)-7/3-5 =-8/-2 so m=4 y-7=4(x-5) y-7=4x-20 y=4x-13

6. A pair of lines are perpendicular if the product of their gradients is m1xm2=-1

   • To find the equation of a line perpendicular to the line, replace the gradient with a negative reciprocal of it.
     • for example if line 1 is y = 2x +3 and you need to find the line perpendicular to this that goes through the point (0,1), then the gradient m = -1/2 (because 2 x -1/2 = -1).

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