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*** S.Gudder

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Analytic Geometry

 We know Geometry is one of the most ancient branches of mathematics. The big step forward in geometry after the Greeks, was the development of a new method called Co-ordinate geometry or Analytical geometry. Modern analytical geometry is also called "Cartesian" after the name of Rene Decartes (1596-1665). In co-ordinate geometry, we enlist the services of Algebra in aid of Geometry.

Some Important Results from Analytic Geometry

Distance Formula

 

The distance between two points  and  is

, where the square root is taken to be positive.

Distance of any point P(x,y) from the origin is

 

Section Formula

Coordinates of the point P(x, y) dividing the segment joining the points  and  in the ratio l: m (internally) are given by

 

Mid-point Formula

 

If P (x, y) is the mid-point of a line segment with end points   and  ,we put, l=m in the formulas of the above result . Then,  

 

Centroid of a Triangle

 

 

Let ,and  be the vertices of the .

Then, the centroid is G =

 

In-centre of a triangle

 

 

Let ,and  be the vertices of the  and a, b, c be the lengths of the sides BC, CA, AB respectively.

Then, the In-centre I =