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)
B
(0, 8)
C
(0, 5)
D
(0, 2)

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).Maths

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