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Question
The line x – 6y + 11 = 0 bisects the join of (8, −1) and (0, k). Find the value of k.
Solution
The given line bisects the join of A(8, −1) and B(0, k), so the co-ordinates of the mid-point 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
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