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Question
Does the line 3x − 5y = 6 bisect the join of (5, −2) and (−1, 2)?
Solution
The given line will bisect the join of A(5, −2) and B(−1, 2), if the co-ordinates of the mid-point of AB satisfy the equation of the line.
The co-ordinates of the mid-point of AB are
`((5 - 1)/2, (-2 + 2)/2)`
= `(4/2, 0/2)`
= (2, 0)
Substituting x = 2 and y = 0 in the given equation, we have:
L.H.S. = 3x − 5y
= 3(2) − 5(0)
= 6 − 0
= 6 = R.H.S.
Hence, the line 3x − 5y = 6 bisect the join of (5, −2) and (−1, 2).
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