maths

• changing into dy/dx form:

  • make sure there's no fractions
  • differentiate
• perpendicular bisector:

  • find midpoint
  • calculate gradient
  • use m1 x m2 = -1
  • sub midpoint into y-b=m(x-a)
• gradient:

  • m = y2-y1/x2-x1
• equations of straight line:

  • y=mx+c
  • y-b=m(x-a)
• finding the positive direction:

  • m=tan(theta)
• collinearity:

  • find both gradients
  • since ... = ... and they share a common point ... the points are collinear
• calculate length (distance):

  • use distance formula= root(x2-x1)^2+(y2-y1)^2
  • keep as surd
• midpoint is the average of both points
• equation of median:

  • find midpoint
  • calculate gradient
  • sub midpoint into y-b=m(x-a)
• altitude:

  • find gradient of bottom points
  • use m1 x m2 = -1
  • sub top point into y-b=m(x-a)