Let the points be A(3,−4) and B(5,2) and mid point of AB=(4,−1). It is given that the bisecting line intercept the co-ordinate axes in the ratio 2:1. ∴ Point of co-ordinate axes are (2k,0) and (0,k). The equation of line passing through the above point is y−0=
k−0
0−2k
(x−2k) ory=−
1
2
(x−2k) ...(i) Since, it is passing through the mid point of AB i. e., (4,−1) ⇒−1=−
1
2
(4−2k) ⇒2=4−2k ⇒ k = 1 Putting the value of k in Eq. (i), we get y=−