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}`
0 Comments