True length by change of plane

Statement. Segment AB has A(0, 2, 2) and B(6, 5, 6). Find its true length with a change of plane.

Step-by-step solution

Draw A and B with their projections and join A'B' and A''B''.
Draw a new ground line parallel to the horizontal projection A'B'.
Carry the heights of A and B perpendicular to the new ground line, keeping the distance.
The new vertical projection A''1B''1 is in true length: measure it on paper.

True length = sqrt(6^2 + 3^2 + 4^2) = sqrt(61) = 7.81 units.