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# Coordinate Revision

### 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

### 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

### 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

### Triangles

Mediator (perpendicular Bisector)

3) Find Midpoint of AB
4) Use the midpoint coordinates to find the Mediator Equation
Altitude