Find the point on y-axis which is equidistant from the points (3, 1, 2) and (5, 5, 2).
Given: Points are A(3, 1, 2) and B(5, 5, 2)
To find: the point on y-axis which is equidistant from the points
As we know x = 0 and z = 0 on y-axis
Let R(0, y, 0) any point on the y-axis
According to the question:
RA = RB
⇒ RA2 = RB2
Formula used:
The distance between any two points (a, b, c) and (m, n, o) is given by,
Therefore,
The distance between R(0, y, 0) and A(3, 1, 2) is RA,
Distance between R(0, y, 0) and B(5, 5, 2) is RB,
As RA2 = RB2
13+ (y – 1)2 = (y – 5)2 + 29
⇒ y2+ 1 – 2y + 13 = y2+ 25 – 10y + 29
⇒ 10y – 2y = 54 – 14
⇒ 8y = 40
⇒ y = 5
Hence point R(0, 5, 0) on y-axis is equidistant from (3, 1, 2) and (5, 5, 2)