Projection of Points, Lines and Planes
This domain tests the geometry of points, straight lines and planes in space and their two-dimensional projections.
Points
A point is located by its distance above or below HP and in front of or behind VP. In first angle, the front view lies above XY when the point is above HP; the top view lies below XY when the point is in front of VP. A point 30 mm above HP and 40 mm in front of VP has its front view 30 mm above XY and its top view 40 mm below XY.
Lines
A line has true length (TL), inclination θ to HP and φ to VP, and traces HT and VT. If a line is parallel to VP, its front view is TL and its top view is TL cos θ. If parallel to HP, its top view is TL and its front view is TL cos φ. If inclined to both planes, neither view is TL; use the rotating-line or auxiliary-plane method. HT is where the line meets HP; VT where it meets VP.
Planes
A plane is shown by its traces. A plane perpendicular to HP and VP is a profile plane. An inclined plane appears as a line in the view perpendicular to its edge; its true shape appears when viewed perpendicular to the plane.
Worked example
Line AB is 70 mm long, parallel to VP, inclined 30° to HP, with A on HP. Because it is parallel to VP, the front view is the true length: 70 mm at 30° to XY. The top view is 70 cos 30° = 60.6 mm, parallel to XY. Reasoning: the inclination to HP shortens only the plan, not the elevation.
Traps
Swapping θ and φ; treating a foreshortened view as true length; putting traces on the wrong side of XY; forgetting that a line parallel to both planes shows TL in both views.