SHORT NOTES: Cartesian system of rectangular coordinate

Cartesian Coordinates:

Polar coordinate:

$x=r\cos \theta \ y=r\sin \theta$

Distance formula:

Distance between two points $P\left ( x_1,y_1 \right )$ and $Q\left ( x_2,y_2 \right )$ is

$d=\sqrt{\left ( x_2-x_1 \right )^2+\left ( y_2-y_1 \right )^2}$

Section formula:

$\left ( \frac{m_1x_2+m_2x_1}{m_1+m_2},\frac{m_1y_2+m_2y_1}{m_1+m_2} \right )$ (internal division)

$\left ( \frac{m_1x_2-m_2x_1}{m_1-m_2},\frac{m_1y_2-m_2y_1}{m_1-m_2} \right )$ (external division)

Shift of origin:

$x=a+x'\cos \phi-y'\sin\phi \\ y=b+x'\sin\phi+y\cos\phi$

where x,y are old coordinates and x',y' are new coordinates.

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