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प्रश्न
The line y = 3x – 2 bisects the join of (a, 3) and (2, −5), find the value of a.
उत्तर
The given line bisects the join of A(a, 3) and B(2, −5), 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
`((a + 2)/2, (3 - 5)/2)`
= `((a + 2)/2, (-2)/2)`
= `((a + 2)/2, -1)`
Substituting `x = (a + 2)/2 ` and y = –1 in the given equation, we have:
y = 3x – 2
`-1 = 3 xx (a + 2)/2 - 2`
`3 xx (a + 2)/2 = 1`
`a + 2 = 2/3`
`a = 2/3 - 2`
= `(2 - 6)/3`
= `(-4)/3`
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