Coordinate Geometry
Gradient
$m=\dfrac{y_1-y_2}{x_1-x_2}$
Equation
$y-y_1=m(x-x_1)$
$y=mx+c$
$y=mx+c$
Midpoint
$\left(\dfrac{x_1+x_2}{2}, \dfrac{y_1+y_2}{2}\right)$
Parallel Lines
$m_1=m_2$
Perpendicular Lines
$m_1=-\dfrac{1}{m_2}$
$m_1\times m_2=-1$
$m_1\times m_2=-1$
Area Of Quadrilateral
$A=\frac{1}{2}\left| \begin{array}{ccccc} x_1 & x_2 & x_3 & x_4 & x_1\\
y_1& y_2 & y_3 & y_4 & y_1\end{array} \right|$
$=\frac{1}{2}|(x_1y_2+x_2y_3+x_3y_4+x_4y_1)$
$-(x_2y_1+x_3y_2+x_4y_3+x_1y_4)|$
Note: coordinates should be in anti-clockwise direction
y_1& y_2 & y_3 & y_4 & y_1\end{array} \right|$
$=\frac{1}{2}|(x_1y_2+x_2y_3+x_3y_4+x_4y_1)$
$-(x_2y_1+x_3y_2+x_4y_3+x_1y_4)|$
Note: coordinates should be in anti-clockwise direction
Circle
$(x-a)^2+(y-b)^2=r^2$
$(a,b)$: centre of circle
$r$: radius
$(a,b)$: centre of circle
$r$: radius
Circle (Second Formula)
$x^2+y^2+2gx+2fy+c=0$
$(-g,-f)$: centre of circle
$\sqrt{f^2+g^2-c}$: radius
$(-g,-f)$: centre of circle
$\sqrt{f^2+g^2-c}$: radius
