COORDINATE GEOMETRY

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COORDINATE GEOMETRY

• Summary

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Distance between two points.In general,
y
B(x2,y2)
AB2 (y2-y1)2 (x2-x1)2
y2
Hence, the formula for Length of AB or Distance
between A and B is
Length y2 y1
y1
A(x1,y1)
Length x2 x1
x
x1
x2
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The mid-point of two points.
Look at its horizontal length
y
B(18,17)
Mid-point of AB
y2
Look at its vertical length
Formula for mid-point is
y1
A(5,3)
x
x1
x2
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GradientIn general,
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Equation of Straight Line
  Equation of a straight line (gradient-intercept
form) y mx c where m is the gradient and
c is the y-intercept.  
  Equation of a straight line (given gradient and
1 point)  
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Collinear Points
3 points are collinear if gradient AB gradient
BC
C
B
A
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Perpendicular Lines

• Two lines with gradients m1 and m2 are
  perpendicular if

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Perpendicular Bisector

• Bisector means to cut (bisect) the line into 2
  equal parts

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Perpendicular Bisector
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Area
Area of a Polygon. Three points
, and . The area of
triangle ABC is given by   This formula may
be extended to a n sided polygon with n vertices.
The area is then given by
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Equation of Circles
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General Form
where r is the radius and (a, b) is the centre.
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Centre (0, 0), radius 1
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Centre (4, -3) and circle touches x-axis

• Radius 3

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Example

• Given equation of circle is ,
• find its centre and radius.
• Centre is (3, 2) and radius is 2