Nayland College  Mathematics Home . Year 9 . Year 10 . Level 1 . Level 2 . L3 Statistics . L3 Maths . L3 Calculus . About . Links 
Coordinates HOME  Achievement Objectives  Distance  Gradient  Rearranging  Equations  Parallel & Perpendicular  Collinear  Applications  Revision 
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 = ^{62}/_{53} 
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 
eg. Find the equation of the line joining (3,6) to (8,2)  

Substitute in values ^{yy1}/_{xx1} = ^{y1y2}/_{x1x2}  ^{y6}/_{x3} = ^{62}/_{38} 
^{y6}/_{x3} = ^{4}/_{5}  
multiply by (x  3) 
y  6 = ^{4(x3)}/_{5} 
multiply by  5 
5(y  6) = 4(x  3) 
Expand brackets 
5y + 30 = 4x  12 
Rearrange so '= 0' 
4x + 5y  42 = 0 
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}/_{3}x  7 
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 