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Nayland College - Mathematics

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Coordinate Revision

Coordinates HOME | Achievement Objectives | Distance | Gradient | Rearranging | Equations | Parallel & Perpendicular | Collinear | Applications | Revision

Link to Exam Papers

Equation of a line y = mx + c

eg. Find the equation of the line joining (3,2) to (5,6)
  y = mx + c
1) Find the gradient of the line m = rise/run
m = 6-2/5-3
  m = 4/2
  m = 2
  y = 2x + c
 
2) Substitute in one coordinate to find 'c'
x = 3 & y = 2
2 = 2x3 + c
  2 = 6 + c
  c = -4
 
3) Equation of line is... y = 2x - 4

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Equation of a line ax + by + c = 0

eg. Find the equation of the line joining (3,6) to (8,2)
Substitute in values y-y1/x-x1 = y1-y2/x1-x2
y-6/x-3 = 6-2/3-8
  y-6/x-3 = 4/-5
multiply by (x - 3)
y - 6 = 4(x-3)/-5
multiply by - 5
-5(y - 6) = 4(x - 3)
Expand brackets
-5y + 30 = 4x - 12
Rearrange so '= 0'
4x + 5y - 42 = 0

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Parallel & Perpendicular Lines

Parallel lines have the same gradient y = 2x + 5
y = 2x - 4
Perpendicular lines have gradients which multiply to -1
'Negative inverse'
y = -3x + 6
y = 1/3x - 7

 

Collinear Points

Test for collinear points  
Gradient AB = Gradient AC? yes = collinear

 

 

Triangles

Mediator (perpendicular Bisector)

1) Find Gradient of AB
2) Find Perpendicular gradient
3) Find Midpoint of AB
4) Use the midpoint coordinates to find the Mediator Equation
Altitude

1) Find Gradient of AB
2) Find Perpendicular gradient
3) Use coordiantes of C to find Altitude Equation
(to find length of altitude find the equation of AB & the altitude and solve simultaneously to find coordinates of intersection)
Median

1) Find Midpoint of AB
2) Use coordiantes of C to find Median Equation

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