True length in perspective relative to the picture plane In a perspective setup, any line that lies entirely in the picture plane is shown at its true length in the final drawing.

Introduction / Context: Perspective drawing simulates human visual perception by projecting 3D points to a 2D plane from a single station point. While most receding lines shorten and converge to vanishing points, some special cases preserve true size and shape, providing essential anchors for accurate construction.

Given Data / Assumptions:

• The picture plane is the plane of projection.
• A straight line segment lies entirely within this plane.
• Standard central (linear) perspective is used.

Concept / Approach: Central projection maps points by drawing rays from the station point through the object to the picture plane. If a line already lies in the picture plane, the mapping of each of its points is identity; therefore the segment retains its true length and orientation. Only geometry not in the picture plane is foreshortened or distorted by perspective.

Step-by-Step Solution:

Verification / Alternative check: Construct a simple grid directly on the picture plane; its edges appear undistorted in the perspective image, confirming the principle.

Why Other Options Are Wrong: Restricting to vertical or horizon-parallel lines is unnecessary; the condition depends on coplanarity with the picture plane, not direction. Claiming it is “never true” ignores the identity mapping case.

Common Pitfalls: Confusing “parallel to the picture plane” with “in the picture plane.” Only lines lying in the plane, not merely parallel to it, remain true length.

Final Answer: Correct