Question

find the co ordinates of point which trisects the line segment joining the point P(2,5) , Q(3,7)

Answer 1

P———R———S———Q

here two points R and S trisect the line joining points P and Q

point R divide the line in 1 : 2 ratio
use section formula,
x-co-ordinate of R
x =(1×3+2×2)/3 = 7/3

y-co-ordinate of R
y=(1×7+2×5)/3 =17/3

hence , R =(7/3 , 17/3)

point S divide the line in 2:1 ratio
x-co-ordinate of S
x =(2×3+1×2)/3 = 8/3

y-co-ordinate of S
y=(2×7+1×5)/3 =19/3

hence, point S =(8/3 , 19/3)