Some important formulas of coordinate geometry

Some important formulas of coordinate geometry :

Distance between two points (x_1,y_1) and (x_2,y_2)

= \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

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Distance of a point (x_1,y_1) from the center (0,0)

= \sqrt{x_1^2+y_1^2}

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Coordinate of a point , who divides a line joining the two points (x_1,y_1) and (x_2,y_2) in ratio of m_1 : m_2

Internal division (\frac{m_1x_2+m_2x_1}{m_1+m_2},\frac{m_1y_2+m_2y_1}{m_1+m_2})

External division (\frac{m_1x_2-m_2x_1}{m_1-m_2},\frac{m_1y_2-m_2y_1}{m_1-m_2})

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Mid point formula : Mid point coordinate of a  line segment by joining two points (x_1,y_1) and (x_2,y_2) is :

=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})

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