Find the point on x-axis which is equidistant from the points A(3, 2, 2) and B(5, 5, 4).

Given: points A(3, 2, 2) and B(5, 5, 4)

To find coordinates of a point on x-axis which is equidistant from given points.

Formula used:

The distance between any two points (a, b, c) and (m, n, o) is given by,

As, y and z coordinate on x-axis are zero

Let point D any point on x-axis be (x, 0, 0)

AD = BD

Distance between B(5, 5, 4) and D(x, 0, 0) is BD,

Distance between A(3, 2, 2) and D(x, 0, 0) is BD,

As, AD = BD

⇒ AD² = BD²

8 + (3 – x)² = 41 + (5 – x)²

⇒ 8 + 9 + x² – 6x= 41 + 25 + x² – 10x

⇒ 17 – 6x = 66 – 10x

⇒ 10x – 6x = 66 - 17

⇒ 4x = 49

Hence, coordinates of point D are