A point C(x,y) is present between A(x _{1},y_{1}) and B(x_{2},y_{2}). C divides AB internally in the ratio m:n. Then the coordinate of C is given by_{2}+nx_{1})/(m+n)] , [(my_{2}+ny_{1})/(m+n)] )
Example:
If C divides AB externally in the ratio m:n. Then the coordinate of C is given byC divides AB internally in the ratio 1:2. A(3,5) and B(1,2). Find C. Let the coordinate of C be (x,y). Then Here m=1, n=2, x _{1}= 3, x_{2} = 1, y_{1} = 5, y_{2} = 2.= 7/3 y= (1×2 + 2×5)/(2+1) = 12/3 = 4. _{2}− nx_{1})/(m − n)] , [(my_{2}− ny_{1})/(m − n)] )
Example:
C divides AB externally in the ratio 2:1. A(3,5) and B(1,2). Find C. Let the coordinate of C be (x,y). Then Here m=2, n=1, x _{1}= 3, x_{2} = 1, y_{1} = 5, y_{2} = 2. = −1 y = (2×2 − 1×5)/(2 − 1) = −1 Section formula in three dimensional coordinate system A point C(x,y,z) is present between A(x _{1},y_{1},z_{1}) and B(x_{2},y_{2},z_{2}). C divides AB internally in the ratio m:n. Then the coordinate of C is given byC≡( [mx _{2}+nx_{1})/(m+n)] , [(my_{2}+ny_{1})/(m+n)] , [(mz_{2}+nz_{1})/(m+n)] )Similarly we can find the coordinates of the point when it divides externally as done in two dimensional. |