Question
Does the line 3x − 5y = 6 bisect the join of (5, −2) and (−1, 2)?
✓
Answer
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
$\left(\frac{5-1}{2}, \frac{-2+2}{2}\right)=(2,0)$
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).
line.
The co-ordinates of the mid-point of AB are
$\left(\frac{5-1}{2}, \frac{-2+2}{2}\right)=(2,0)$
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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