Question

the line bisects the join of (k,-1) and (0,6). find the value of k​

Answer 1

Answer :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=

0−2k

k−0

(x−2k)

or y=−

2

1

(x−2k) ..... (i)

Since, it is passing through the mid point of AB i.e., (4,−1)

⇒−1=−

2

1

(4−2k)

⇒2=4−2k

⇒k=1

Putting the value of k in Eq. (i), we get

y=−

2

1

(x−2)

⇒x+2y=2