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Co-Ordinate Geometry & Simultaneous Equations Cheat Sheet by

Cheat Sheet for Co-Ordinate Geometry & Simultaneous EquationsEnjoy :)

Sket­ching Straight Lines

Using x & y intercepts | C cannot be equal to 0
Gradient - intercept method
ax + by = c --> e.g 2x - 5y = 10
y = mx + c
y = 0 when solving x
Horizontal Line
2x - 0 = 10
gradient = 0
x = 5
y = c
x = 0 when solving y
Vertical Line
2(0) - 5y = 10
gradient = undefined
-5y = 10
x = a
y = 10/-5
a --> x-inte­rcept
y = -2
 

Finding the equation of a straight line

Gradient + y-inte­rcept
Gradient + a point (x1, y1)
2 points (x1, y1) (x2, y2)
Distance between 2 points
Sub into equation
Sub into equation
1st find m
Sub into equation
y = mx + c
y - y1 = m(x - x1)
m = y2 - y1/x2 - x1
AB = √(x2 - x1)² + (y2 - y1)²
Example
Example
2nd sub into equation
Example
c = 5 | m = -1
m = 2 | (2, -0.5)
y - y1 = m(x - x1)
A = (3, -5) | B = (-2, 1)
y = -1x + 5
y + 0.5 = 2(x - 2)
Example
AB = √(-2 - 3)² + (1 - -5)²
 
y + 0.5 = 2x - 4
(-1, 4) , (5, 2)
AB = √(-5)² + 6²
 
y = 2x - 4.5
m = 2 - 4/3 - (-1)
AB = √25 + 36
  
m = -2/4 --> -1/2
AB = √61
  
y - 4 = -1/2(x - - 1)
  
y - 4 = - 1/2x - 1/2
  
y = - 1/2x + 7/2
 

Middle point of a line

Middle point of a line
Paralell Lines
Perpen­dicular Lines
Sub into equation - i.e / means divide
Sub into equation
Sub into equation
M = (x1 + x2/2, y1 + y2/2)
m1 = m2
m1 x m2 = -1 or m2 = 1/m1
Example
Example - 1st find m (gradient)
Example - 1st find m (gradient)
(3, 5) | (2, 7)
A (4, 13) | B (2, 9)
A (-4, 9) | B (2, -6)
M = 3 + 2/2, 5 + 7/2
mAB = 9 - 13/2 - 4
mAB = -6 - 9/2 - (-4)
M = (5/2, 12/2)
mAB = -4/-2
mAB = -15/6
M = (5/2, 6)
mAB = 2
mAB = -5/2
 
C (0, -10) | D (15, 0)
C (-5, 8) | D (10, 14)
 
mCD = 0 - (-10)/15 - 0
mCD = 14 - 8/10 - (-5)
 
mCD = 10/15
mCD = 6/15
 
mCD = 2/3
mCD = 2/5
 
∵ mAB ≠ mCB
2nd | sub into m1 x m2 = -1
 
∴ not parralell
-5/2 x 2/5 = -1
  
-10/10 = -1
  
∴ AB ⊥ CD
   
 

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