Show that the points (1, 1, 1) and (–3, 0, 1) are equidistant from the plane 3x + 4y – 12z + 13 = 0.

Question

Philoid · Accepted Answer

Given:

* Points: A(1, 1, 1) and B(–3, 0, 1)

* Plane: π = 3x + 4y – 12z + 13 = 0

We know, the distance of point (x₁,y₁,z₁) from the plane

is given by:

⟹ Distance of (1,1,1) from the plane =

= units

⟹ Distance of (–3,0,1) from the plane =

= units

∴ the points (1, 1, 1) and (–3, 0, 1) are equidistant from the plane

3x + 4y – 12z + 13 = 0.