# Find the point on the y-axis which is equidistant from the points

Question:

Find the point on the y-axis which is equidistant from the points A(3, 1, 2) and B(5, 5, 2).

Solution:

Consider, C(0,y,0) point which lies on y axis and is equidistant from points A(3, 1, 2) and B(5, 5, 2).

∴ AC = BC

$\sqrt{(0-3)^{2}+(y-1)^{2}+(0-2)^{2}}=\sqrt{(0-5)^{2}+(y-5)^{2}+(0-2)^{2}}$

Squaring both sides,

$(0-3)^{2}+(y-1)^{2}+(0-2)^{2}=(0-5)^{2}+(y-5)^{2}+(0-2)^{2}$

$9+y^{2}-2 y+1+4=25+y^{2}-10 y+25+4$

8y = 40

Y = 5

The point C is (0,5,0).