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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.
 

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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(x1, y1) and B(x2, y2) is given by

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The distance of a point A(x1, y1) from the origin is given by Description: 37278.png


Section formula: The coordinates of a point P, which divides the line joining two points A(x1, y1) and B(x2, y2) in the ratio m:n is given as

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

 

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Midpoint formula: The midpoint of the line joining two points A(x1, y1) and B(x2, y2) is given by

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Refer the figure below:

 

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