`A(4,\ 2),\ B(6,5)` and `C(1,\ 4)` are the vertices of ` A B C` . Find the coordinates of the points `Q` on median `B E` such that `B Q : Q E=2:1`

Options

A. Q=`(11/3,11/3)`
B. Q=`(10/3,11/3)`
C. Q=`(11/3,10/3)`
D. Q=`(10/3,10/3)`

Answer

A

Explanation

let's take a pont D in mid of B and C, E between A and C, F between A and B

co-odenates of D will be

`x_d`=`(6+1)/2`=`7/2`

`y_d`=`(5+4)/2`=`9/2`

so, D=`(7/2, 9/2)`

similarly, E and F will be

E=`(5/2,3)` and F= `(5,7/2)`

Q is on median BE at the ration of 2:1

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