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Question

The point of intersection of y-axis and the perpendicular bisector of line segment joining A (3, 6) and B (-3, 4) is :


A
(0, 3)
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B
(0, 8)
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C
(0, 5)
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D
(0, 2)
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Solution

The correct option is B (0, 5)
Let y axis meets the perpendicular bisector of AB at the point $$ P(0, y) $$
$$ PA = PB $$
$$ {PA}^{2} = {PB} ^{2} $$
$$ {(30)}^{2} + {(6y)}^{2} = {(30)}^{2} + {(4y)}^{2} $$
$$ 9 + 36 + {y}^{2}12y = 9 + 16 + {y}^{2} 8y $$
$$ 36 - 12y = 16 - 8y $$
$$ 4y = 20 $$
$$ => y = 5 $$
Therefore the required point is P(0, 5).

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