# Co-ordinate Geometry

The study of geometry using concepts of algebra is known as co-ordinate geometry.We take a pair of perpendicular lines in a plane as reference; the horizontal line is called the x-axis while the vertical line is called the y-axis. The plane containing the two axes is called the co-ordinate plane.

The intersection point of the two axes is called the “origin” and all distances are measured with origin as the starting point. Any point in the plane is represented by a pair of numbers (x, y) which are known as co-ordinates of the point. “x” is the distance of the point from origin along x-axis and ‘y’ is the distance of the point from origin along y-axis.

**Distance formula:** Distance between two points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) is given by

The distance of a point A(x_{1}, y_{1}) from the origin is given by

**Section formula:** The coordinates of a point P, which divides the line joining two points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) in the ratio m:n is given as

If the point P lies outside the line, then it is known as external division and

**Midpoint formula:** The midpoint of the line joining two points A(x_{1}, y_{1}) and B(x_{2}, y_{2}) is given by

Refer the figure below:

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