### Section Formula

 A point C(x,y) is present between A(x1,y1) and B(x2,y2). C divides AB internally in the ratio m:n. Then the coordinate of C is given by C≡( [mx2+nx1)/(m+n)] , [(my2+ny1)/(m+n)] ) Example: C 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, x1= 3, x2 = 1, y1 = 5, y2 = 2. x = (1×1 + 2×3)/(2+1) = 7/3   y= (1×2 + 2×5)/(2+1) = 12/3 = 4. Hence the coordinate of C is (7/3,4). If C divides AB externally in the ratio m:n. Then the coordinate of C is given by C≡( [mx2− nx1)/(m − n)] , [(my2− ny1)/(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, x1= 3, x2 = 1, y1 = 5, y2 = 2. x = (2×1 − 1×3)/(2 − 1) = −1   y = (2×2 − 1×5)/(2 − 1) = −1 Hence the coordinate of C is (−1,−1). Section formula in three dimensional coordinate system A point C(x,y,z) is present between A(x1,y1,z1) and B(x2,y2,z2). C divides AB internally in the ratio m:n. Then the coordinate of C is given by C≡( [mx2+nx1)/(m+n)] , [(my2+ny1)/(m+n)] , [(mz2+nz1)/(m+n)] ) Similarly we can find the coordinates of the point when it divides externally as done in two dimensional.