Rotation onto the horizontal plane

Statement. Point A(3, 4, 5) belongs to plane P: y = 4. Rotate the plane onto the horizontal plane and find the rotated position (A).

Step-by-step solution

The hinge is the horizontal trace of the plane: the line y = 4, z = 0, parallel to the ground line.
Because A' falls on the hinge (the plane is y = 4), the radius of rotation is the height: 5 units.
When rotating, that distance is placed perpendicular to the hinge: the point turns until it lies on the horizontal plane.
The result (A) lies in the plane z = 0, with the same x as A.

(A) is obtained by rotating A around the trace y = 4 until it lies on the horizontal plane.