The equation to the line bisecting the join of (3,-4) and (5,2) and having intercepts on the x-axis and y-axis in the ratio of 2:1 is:

Options

A. x+y-3=0
B. 2x-y=9
C. x+2y=2
D. 2x+y=7

Answer

C

Explanation

Let the points be A (3,-4) and B(5,2)
Mid - point of AB = (4,-1)
It is given that the bisecting line intersect the coordinate axes in the ratio 2 :1 .

So, point on coordinate 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) Rightarrow y = -1/2 (x-2k)`
Since it is passing through the mid-point of AB.i.e. (4,-1)
` -1= -1/2 (4-2k) Rightarrow k = 1`
On putting the value of k in Eq. (i) we get ,
`y= -1/2 (x-2) Rightarrow x +2y =2 `