CO-ORDINATE GEOMETRY

Introduction

* Distance Formula: Formula to find the distance between two points A(x₁, y₁) and

      B(x₂, y₂) is given by

    AB = √((x₂ - x₁)² + (y₂ - y₁)²) ̅ Or AB = √((x₁ - x₂)² + (y₁ - y₂)²) ̅

Note :

* If one of the point being origin i.e., A(0, 0) and B(x, y) then the formula to find the

 distance between them is given by

   AB = √(x² + y²) ̅

* If A (0, y) and B(x, 0) (or) A(x, 0) and B(0, y) then the formula to find the distance

 between them is given by

   AB = √(x² + y²) ̅

* Section Formula => If 'p' divides the line segment which is formed by joining the

    points A(x₁, y₁) and B(x₂, y₂) internally in the ratio m₁:m₂, then the formula

    to find the co-ordinates of 'p' is given by P :-

P= [(m_1 x_2+ m_2 x_1)/(m_1+ m_2 ) ,(m_1 y_2+ m_2 y_1)/(m_1+ m_2 )]

Note :

* If 'p' divides the line segment which is formed by joining the points A (x₁, y₁) and

 B(x₂, y₂) externally in the ratio m₁: m₂, then the formula to find the co-ordinates of

 'p' is given by

P= [(m_1 x_2- m_2 x_1)/(m_1- m_2 ) ,(m_1 y_2- m_2 y_1)/(m_1- m_2 )]

* If 'p' divides the line segment which is formed by joining the points A(x₁, y₁) and

 B(x₂, y₂) in the ratio 1:1, i.e., if 'p' is the mid-point of AB, then the formula to find the

 co-ordinates of 'p' is given by

P= [(x_1+ x_2)/2 ,(y_1+ y_2)/2]

* The general form of any point on x-axis is given by (x, 0)

* The general form of any point on y-axis is given by (0, y)

* If A(x₁, y₁), B(x₂, y₂) and C(x₃, y₃) are the three vertices of a Δ ABC, then the formula

 to find its area is given by

     Δ = 1/2 | x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |

Note:

* If A(0,0), B(x, y) and C(x₂, y₂) are the three vertices of a Δ ABC then the formula to

 find its area is given by

     Δ = 1/2 | x₁y₂ - x₂y₁ |

* If A(0,0), B(x, 0) and C(0, y) are the three vertices of a Δ ABC then the formula to

 find its area is given by

     Δ = 1/2 |xy|

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