Geometry

Geometry

1. Straight line

   • Gradients
     • m=y2-y1/x2-x1
     • m=tanx
   • Distance
     • d=SQRT[(x2-x1)+(y2-y1)]
     • Perpindicular d= Ax+By+C/ SQRT(A^2 + B^2)
   • Collinearity
     • Share common point
     • Same gradient
     • Lie on the same line
   • Perpendicular Lines
     • m1xm2=-1
     • Intersect at right angles
   • Equations
     • y=mx+c c- y intercept
     • y-b=m(x-a) (a,b)
     • Ax+By+C=0 Linear
   • Perpendicular Bisectors
     • Cuts through the midpoint of a line at 90dg.
       • Midpoint= (x1+x2/2,y1+y2/2)

2. Circles

   • Intersection
     • b^2-4ac>0 2pts.
     • b^2-4ac=0 1pt. -Tangent
       • Repeated root= tangent
     • b^2-4ac<0 0pts.
   • Line meets curve
     • Let y=y and solve
   • Equation
     • (x-a)^2+ (y-b)^2=r^2
       • Centre(a,b)
       • Radius- r
     • x2 + y2 + g2x + 2fy + c = 0
       • Centre(-g,-f)
       • r= sqrt(g^2+f^2-c)
   • Concentric circles
     • Same centre
     • Different radius
   • Tangents
     • Perpendicular
       • m1xm2=-1