Coordinates of Points Calculator (Externally/ Internally)

The Coordinates of points is determined a pair of numbers defining the position of a point that defines its exact location on a two-dimensional plane.
Coordinates of Points Calculator (Externally and Internally)
X1: Y1:
X2: Y2:
Ratio
m: n:
     
Coordinates of Point
Formula
Section or Ratio Externally
(mx2-nx1/m-n , my2-ny1/m-n)

Section or Ratio Internally
(mx2+nx1/m+n , my2+ny1/m+n)

Ratio formula or section formula is used to find the coordinates of a point P which divides the segment joining the points A and B internally or externally in the ratio m : n.
Case 1: Find the coordinates of the point which divides the line joining the points (2, 3), (4, 5) internally in the ratio 2:1.
x1 = 2, y1 = 3 and
x2 = 4, y2 = 5
m = 2, n = 1

Apply Formula
(mx2+nx1/m+n , my2+ny1/m+n)
(2*4+1*2/2+1 , 2*5+1*3/2+1)
(8+2/3 , 10+3/3 )
(10/3 , 13/3)
(3.3  , 4.3)

Case 2: Find the coordinates of the point which divides the line joining the points (2, 1), (3, 4) externally in the ratio 2:5.
x1 = 2, y1 = 1 and
x2 = 3, y2 = 4
m = 2, n = 5

Apply formula
(mx2-nx1/m-n  , my2-ny1/m-n)
(2*3-5*2/2-5 , 2*4-5*1/2-5)
(6-10/-3  , 8-5/-3)
(-4/-3 , 3/-3)
(4/3 , -1)