Question 4 of 9: Rotate a labelled pictorial 90° about an edge

Question 4: Rotate a labelled pictorial 90° about an edge

Question text not reproduced: the examination questions are © Engineers and Geoscientists BC. Open the official past paper (linked at the top of this page) to read the question, then follow the worked solution below.

The given solid is a single-slope (shed) roof block: vertices A, H, G, F lie on the front wall/base, edge BC is the back-top ridge, and D, E mark the roof’s far/mid points. Rotating 90° clockwise about BC (looking at face AFGH) swings every OTHER vertex through a quarter turn around that fixed edge, while B and C themselves do not move (they lie on the axis).

Approach. Treat BC as a hinge line. For every vertex not on the axis, its perpendicular distance to line BC stays constant (rotation preserves distance-to-axis and distance-along-axis); only its angular position around BC changes by 90° in the clockwise sense specified. This is most reliably done by resolving each vertex into a component along BC (unchanged) and a component in the plane perpendicular to BC (rotated 90°), i.e. the standard axis-angle (Rodrigues) rotation.

1. Fix the axis. B and C keep their pictorial positions; they define the hinge line for every other vertex.
2. Rotate each free vertex. A, D, E, F, G, H each swing 90° clockwise (as seen looking at face AFGH) about BC, preserving their true distance from the BC line.
3. Re-sketch on the isometric axes. After rotation the face that was AFGH now faces upward/outward toward the observer’s original view direction, and the roof slope that was on top now reads as a side face.