Distance Formula
* The distance between the points ( x_{1} y_{1} ) and ( x_{2} y_{2} ) is given by :
\sqrt{( x_{2} - x_{1} )² + ( y_{2} - y_{1} )²}
* The distance of the point (x, y) from origin is given by :
\sqrt{ x^{2} + y^{2} }
* Three points A, B and C are collinear if AB + BC = AC
Section Formula
The section formula states that any point P(x, y) that divides a line segment in the ratio m:n can be represented as
( \frac{ mx_{2} + nx_{1} }{m + n} , \frac{ my_{2} + ny_{1} }{m + n} )
The following are the corollaries f the section formula :
* The midpoint of a line segment joining ( x_{1} y_{1} ) and ( x_{2} y_{2} ) is:
( \frac{ x_{1} + x_{2} }{2} , \frac{ y_{1} + y_{2} }{2} )
* The centroid G of a triangle, with vertices ( x_{1} y_{1} ), ( x_{2} y_{2} ) and ( x_{3} y_{3} ) is:
( \frac{ x_{1} + x_{2} + x_{3} }{3} , \frac{ y_{1} + y_{2} + y_{3} }{3} )
Area of a Triangle
If A( x_{1} y_{1} ), B( x_{2} y_{2} ) and C( x_{3} y_{3} ) are three vertices of a triangle, then the area
of a triangle is given by :
area of a triangle ABC = \frac{1}{2} \times [ x_{1} ( y_{2} - y_{3} ) + x_{2} ( y_{3} - y_{1} ) + x_{3} ( y_{1} - y_{2} ) ]