Coordinate Geometry (Additional Math)

📈 Gradient

m=\frac{y_1-y_2}{x_1-x_2}

📝 Equation

$$y-y_1=m(x-x_1)$$

$$y=mx+c$$

📍 Midpoint

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

📏 Parallel Lines

$$m_1=m_2$$

⟂ Perpendicular Lines

m_1=-\frac{1}{m_2}

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

⭕ Circle

$$(x-a)^2+(y-b)^2=r^2$$

$(a,b)$: 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