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)

Answer 1

Answer: (C)

(0, 5)

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