Question

P is the mid point of the line segment joining the point A(-3,7) and B(9,-1) . Find the co ordinate of point P. Further , if R(2,2)divides the line segment joining P and the origin in the ratio m:n . Find the ratio m:n

Answer 1

Answer:

let A(x1,y1) and B(x2,y2)

by midpoint formula

coordinate of point p will be

x=x1+x2÷2

x=-3+9÷2

x=6÷2

x=3

y=y1+y2÷2

y=7-1÷2

y=6÷2

y=3

therefore coordinates of point p is (3,3)

the coordinates of origin O is (0,0)

let o(x3,y3) and R (x4,y4)

by section formula

coordinates of point r is

x4=m×x +n×x3 ÷m+n

2=m×3 + n×0 ÷m+n

2m + 2n = 3m

2n = m

therefore m:n =2:1

therefore point R divides segment in 2:1