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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