Question

The line x – 6y + 11 = 0 bisects the join of (8, −1) and (0, k). Find the value of k.

Answer 1

The given line bisects the join of A(8, −1) and B(0, k), so the coordinates of the midpoint of AB will satisfy the equation of the line. 

The co-ordinates of the mid-point of AB are

`((8 + 0)/2, (-1 + k)/2) = (4(-1 + k)/2)`

Substituting x = 4 and `y = (-1 + k)/2` in the given equation, we have:

x − 6y + 11 = 0

`4 - 6((-1 + k)/2) + 11 = 0`

`6((-1 + k)/2) = 15`

`(-1 + k)/2 = 15/6`

`(-1 + k)/2 = 5/2`

−1 + k = 5

k = 6