Co-ordinate geometry

Co-ordinate geometry

1. The gradient is given by Δy/Δx.

2. If two lines' gradients are equal, they are parallel.

3. M1 x M2 = -1

   • If the gradients multiplied together equal negative 1, they are perpendicular.

4. When points A and B have co-ordinates (x,y) and (w,z)...

   • Distance AB = √(w-x)²+(z-y)²
   • Midpoint of line AB = ((x+y)/2, (w+z)/2)

5. The equation of a straight line can take any of the following forms:

   • Line parallel to the y axis: x=a
   • Line parallel to the x axis: y=b
   • Line through the origin with the gradient m: y=mx
   • Line through (0,c) with the gradient m: y=mx+c
   • Line through (x1,y1) with gradient m: y-y1=mx(x-x1)

6. The equation of a circle with centre (h,k) and radius r is:

   • (x-h)²+(y-k)²=r²

7. When the centre is at the origin this simplifies to:

   • x²+y²=r²