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1
Distance between two points with coordinates (a,b), (c,d)
$$\sqrt{\left(a-c\right)^2+\left(b-d\right)^2}$$
2
Slope of the line joining the points (a,b) and (c,d)
$$\dfrac{d-b}{c-a}$$
3
Midpoint of the line segment joining (a,b) and (c,d)
$$\left(\dfrac{a+c}{2},\dfrac{b+d}{2}\right)$$
4
Two lines with slopes m and n are perpendicular then
$$m\times\ n=-1$$
5
Length of the perpendicular from (m,n) on the line ax + by + c = 0 is
$$\dfrac{\left(am+bn+c\right)}{\sqrt{\ a^2+b^2}}$$
6
Distance between two parallel lines ax + by + c = 0 and ax + by + d = 0 is
$$\dfrac{\left|d-c\right|}{\sqrt{\ a^2+b^2}}$$
7
Coordinates of a point P that divides the line joining A (m,n) and B (r,s) internally in the ratio x:y
$$\left(\dfrac{xr+ym}{x+y},\dfrac{xs+yn}{x+y}\right)$$
8
Centroid of a triangle with coordinates (a,b), (c,d), (e,f) is
$$\left(\dfrac{a+c+e}{3},\dfrac{b+d+f}{3}\right)$$
9
If the equation of circle is given by $$x^2+y^2+2gx+2fy+c=0$$, Centre is given by
(-g,-f)
10
If the equation of circle is given by $$x^2+y^2+2gx+2fy+c=0$$, Radius of the circle is given by
$$\sqrt{\ g^2+f^2-c}$$
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