Projections of Points and Lines Questions and Answers

Answer: A

Correct answer: both the assertion and the reason are true and the reason explains the assertion

Both are true and the reason is the whole of the explanation. Orthographic projection preserves length only along directions parallel to the plane of projection, so a line not parallel to a given plane is shortened in that view. A line inclined to both principal planes is parallel to neither, so both views shorten it and an auxiliary parallel to the line is needed.

Answer: B

Correct answer: the assertion is false, the sum never exceeding 90 degrees

The two inclinations are not independent: they are the angles a single direction makes with two mutually perpendicular planes, and for any such direction \( \theta + \phi \le 90^\circ \). The sum reaches ninety only when the line lies in a profile plane. A stated pair summing to more than ninety describes no line and indicates an error in the data.

Answer: C

Correct answer: works from the projected length and the height difference

The trapezoidal method takes what the views already give - the length in plan and the difference in height between the ends - and treats them as the two perpendicular sides of a right triangle whose hypotenuse is the true length. Nothing is swung or reprojected, which is why it is the quicker of the two constructions.

Answer: D

Correct answer: a line perpendicular to the vertical plane

The elevation is the view onto the vertical plane, so a line appears there as a point only when it is perpendicular to that plane and therefore seen end on. A line perpendicular to the horizontal plane gives a point in the plan instead, and the other two are foreshortened rather than reduced to a point.