Geometry Formulas

Geometry formulas contains various concepts related formulas of mathematical stream geometry like slope , section formula , midpoint formula , etc.

1) Distance Formula

In the figure , $A (x_1, y_1)$ and $B(x_2, y_2)$ are anyt wo points in the XY plane, distance between A and B is given by ,

$d(A,B)=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

This is Distance formula.

Note : Co-ordinates of origin are $(0, 0)$ and  if co-ordinates of point A are $(x, y)$ then distance between origin and point A is 

$d(O, A) =\sqrt{ x_2 + y_2} $.

2) Section Formula 

In the figure , point P on the seg AB in $XY$ plane, divides seg $AB$ in the ratio $m : n$ and assume $A(x_1,y_1),  B(x_2,y_2)$ and  $P(x, y)$ 

So, co-ordinates of the point P, which divides the line segment joining the points $A(x_1, y_1)$ and $B(x_2, y_2)$ in the ratio $m : n$ are given by ,

$(\frac{mx_2+nx_1}{m+n},\frac{my_2+ny_1}{m+n})$

3) Midpoint Formula

If $A(x_1, y_1)$ and $B(x_2, y_2)$  are two points and $P (x, y)$ is the midpoint of seg $AB$ then $m = n$, the co-ordinates of midpoint P is,

$x=\frac{x_1+x_2}{2}$ and $y=\frac{y_1+y_2}{2}$

4) Centroid Formula

In $\triangle ABC $, $A(x_1, y_1), B(x_2, y_2), C(x_3, y_3)$ are the vertices. Seg $AD$ is a median and $G(x, y)$ is the centroid, then

So co-ordinates of the centroid G are $(\frac{x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3})$

5) Slope Formula

If $ A(x_1, y_1)$ and $B(x_2, y_2)$  are any two points on line $l$, the ratio $\frac{y_2-y_1}{x_2-x_1}$  is called the slope of the line $l$.

Generally slope is shown by letter $m$.

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