Projections of Points and Lines Questions and Answers

Answer: C

Both projections foreshorten it, so the true length must be found by construction rather than measured off either view. Rotation, the trapezoidal method and the auxiliary plane are the three standard ways of obtaining it.

Answer: D

Correct answer: greater than its true inclination

A projection shortens the line while preserving the height or depth difference between its ends, so the same rise is spread over a shorter base and the angle measured in the view is steeper than the real one. That is why an inclination read straight off the plan overstates the truth, and why the true length must be found first.

Answer: A

Correct answer: rotating it parallel to a principal plane

The rotation method swings one end of the line about the other until the line lies parallel to a plane of projection, keeping its length unchanged throughout. In its new position it projects at true length onto that plane, and the angle it then makes with the reference line is its true inclination.

Answer: B

Correct answer: hypotenuse of a triangle on the projected length

The trapezoidal method erects the height differences of the two ends perpendicular to the projected line and joins their tops. The projected length and the difference in height are the two perpendicular sides of a right triangle, and the true length is the hypotenuse - which is simply Pythagoras applied to the geometry of the projection.

Answer: C

Correct answer: parallel to the line itself

A line projects at true length onto any plane parallel to it, so the auxiliary is set parallel to the line and the view taken on it gives the length directly. Setting the auxiliary perpendicular to the line would give the opposite result - the line seen end on as a point.

Answer: D

Correct answer: horizontal plane

The traces of a line are the points at which it pierces the planes of projection: the horizontal trace where it meets the horizontal plane and the vertical trace where it meets the vertical. Both may require the line to be produced beyond its given ends, and together they fix the line completely.

Answer: A

The trace is a point in the horizontal plane, so its height above that plane is zero and its elevation cannot leave the line. Locating it is a matter of producing the elevation of the line until it meets the reference line.

Answer: B

Correct answer: no horizontal trace

A line parallel to the horizontal plane never meets it, however far it is produced, so it has no horizontal trace. It does meet the vertical plane, so it has a vertical trace. The mirror case is a line parallel to the vertical plane, which has a horizontal trace and no vertical one.

Answer: C

Correct answer: on the reference line

A line lying in the vertical plane can only meet the horizontal plane where the two planes themselves meet, which is the reference line. Its horizontal trace therefore lies on the reference line, and its plan lies along that line as well - the whole line being at zero distance in front of the vertical plane.

Answer: D

Correct answer: on the corresponding traces of the plane

If a line lies in a plane then the point where the line pierces the horizontal plane must also be a point of the plane, and so must lie on the plane’s horizontal trace; the same argument applies to the vertical. This is the standard construction for drawing a plane through a given line.