Question

Find the coordinates of point Q and R on median BE and CF respectively. such that BQ:QE is equal to 2:1 CR:RF is equal to 2:1

Answer 1

The coordinates of Q and R are (11/3 , 11/3).

As per the question, the coordinates of E and F can be found as below:

• As BE is the median, E is the mid-point of AB. Therefore,

• E = [ (4+1) / 2, (2+4) /2 ]

           = (5/2,6/2)

           = (5/2,3)

• As CF is the median, F is the mid-point of AB.

• F = [ (4+6) / 2, (2+5) / 2 ]

           = (10/2,7/2)

           = (5,7/2)

• Now, as R lies on CF, therefore by applying section formula, we get,

        R =  [ ( 2(5) + 1(1) ) / (2+1) ,  ( 2(7/2) + 1(4) ) / (2+1) ]

          = (11/3 , 11/3)

• Also, Q lies on BE, therefore by applying section formula, we get,

        Q =  [ ( 2(5/2) + 1(6) ) / (2+1) ,  ( 2(3) + 1(5) ) / (2+1) ]

           = (11/3 , 11/3)