Straight Lines

Straight Lines

1. Distance Between Points

   • d=√(
   • The distance between any 2 points can be easily worked out using the distance formula

2. The Midpoint

   • The point halfway between two points is called their. It is calculated using the midpoint formula.
   • midpoint= (

3. Gradient

   • The gradient can be worked out in 2 ways
     • m=tanƟ
     • m=
   • The gradient of a line can be seen from its position
     • lines parallel to
     • lines parallel to
     • positive gradients slope up from left to right /
     • negative gradients slope down from left to right \
     • two lines are said to be parallel when they have the same gradient

4. Collinearity

   • Points which lie on the same straight line are said to be collinear
   • To find out if points A B and C are collinear we must work out the gradient of AB and BC
     • if gradient is the same you must end with a conclusion
       • "since mᵃᵇ = mᵇc and B is a common point, points A B and C are collinear"
   • The points must have the same gradient and share a common point

5. Gradient of Perpendicular Lines

   • 2 lines that meet at right angles are said to be perpendicular
   • m×m⟂=-1
     • an easier way to see this is to flip the fraction and swap the sign

6. The Equation of a Straight Line

   • To work out the equation of a straight line we need the gradient (m) and a point which lies on the line
   • Lines parallel to axis
     • if a line is parallel to the
     • if a line is parallel to the
   • to extract the gradient find m

7. Median

   • A median of a triangle is a line through a vertex and the midpoint of the opposite side
   • 1. Calculate the midpoint of the relevant line
     • 2. Calculate the gradient of the median
       • 3. Find equation using gradient and midpoint

8. Altitude

   • The altitude of a triangle is a line through a vertex, perpendicular to the opposite side
   • 1. Calculate gradient of perpendicular side
     • 2. Calculate the gradient of the altitude using m×m⟂=-1
       • 3. Find equation using gradient and a point that altitude passes through

9. Perpendicular Bisectors

   • A perpendicular bisector is a line which cuts through the midpoint of a line at a right angle
   • 1. Calculate midpoint of line being bisected
     • 2.Calculate gradient of line from step 1 and find is perpendicular gradient (m×m⟂=-1)
       • 3. Find equation using point from step 1 and gradient from step 2

10. Intersection of Lines

    • Basically, when you have 2 equations of 2 lines that intersect and you use simultaneous equations to work out
      • Always sum this up by putting the

11. Concurrency

    • Any number of lines are said to be con current if there is a point through which they all pass