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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 ### 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 = 