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in 3D Coordinate Geometry by (55.0k points)
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Find the point on the y-axis which is equidistant from the points A(3, 1, 2) and B(5, 5, 2).

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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

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

Squaring both sides, 

(0 - 3)2 + (y - 1)2 + (0 - 1)2 = (0 - 5)2 + (y - 5)2 + (0 - 2)2

9 + y2 - 2y +1 + 4 = 25 + y2 -10y + 25 + 4 

8y = 40 

Y = 5 

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

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