Let P and Q be any two points find the coordinates of the point R which divides PQ externally - Maths - Introduction to Three Dimensional Geometry

Question

Let P and Q be any two points find the coordinates of the point R
which divides PQ externally in the ratio 2:1 and verify that Q is
the midpoint of PR

Vishvesh Kumar · Accepted Answer

Let coordinate of P and Q are (a,b) and (c,d) respectively 
R divide PQ externally in m:n=2:1 so coordiante of R is 2×c-1×a2-1'2×d-1×b2-1= 2c-a ,2d-bNow coordinate of mid point of PR is  a+(2c-a)2'b+(2d-b)2=c,d=QThis shows that midpoint of PR is Q

Let P and Q be any two points. find the coordinates of the point R which divides PQ externally in the ratio 2:1 and verify that Q is the midpoint of PR.