Projections of Points and Lines Questions and Answers

Answer: C

Correct answer: the plan

A line parallel to the horizontal plane projects onto it without foreshortening, so the plan gives both its true length and its true inclination to the vertical plane. The elevation shows it as a line parallel to the reference line, foreshortened by the cosine of that inclination.

Answer: D

Correct answer: third quadrant

The quadrants are defined by the two planes: first is above and in front, second above and behind, third below and behind, fourth below and in front. Below the horizontal plane and behind the vertical is therefore the third quadrant, in which the plan appears above the reference line and the elevation below it.

Answer: A

Correct answer: 1-Q, 2-P, 3-R

Foreshortening occurs in any view whose plane is not parallel to the line. A line parallel to both planes is parallel to each, so both views give the true length. One parallel to the vertical plane only gives it in the elevation. And one inclined to both is parallel to neither, so neither view gives it and an auxiliary is required.

Answer: B

Correct answer: 1-Q, 2-P, 3-R

Three constructions with three distinct effects. The rotation method swings the line about one end until it lies parallel to a principal plane, where it projects at true length. An auxiliary perpendicular to the line reduces it to a point, which is what a clearance measurement needs. And the trapezoidal method erects the height differences on the plan and takes the hypotenuse.

Answer: C

The true length view must come first because the second auxiliary is set perpendicular to it. Only in the point view is every direction from the line perpendicular to it, which is what makes the measured distance the shortest.

Answer: D

Correct answer: 1 and 2 only are correct

Statements 1 and 2 are correct: a point on the reference line is at zero distance from both planes and so lies in both, and the apparent inclination always exceeds the true one. Statement 3 has the traces the wrong way round - a line parallel to the horizontal plane has no horizontal trace, since it never meets that plane.

Answer: A

Parallelism to the horizontal plane is what preserves the length when viewed from above. A line perpendicular to that plane appears as a point in the plan, and one inclined to both is foreshortened in every principal view.

Answer: B

Correct answer: measuring the longer of the two projected lengths

Both projections of a line inclined to both planes are foreshortened, so the longer of them is still short of the truth and measuring it gives an underestimate. The other three are genuine methods: an auxiliary parallel to the line, the rotation method, and the trapezoidal construction on the plan and the height difference.

Answer: C

Correct answer: too large

A projection preserves the height difference between the ends while shortening the base, so the angle in the view is steeper than the real one. Reading the inclination straight off a view therefore overstates it, and the error grows the more the line is inclined to that plane. The true angle appears only in a view showing the true length.

Answer: D

Correct answer: in the vertical plane

If every point of the line has its plan on the reference line then every point is at zero distance in front of the vertical plane, which means the line lies in that plane. Lying in the horizontal plane would put the elevation on the reference line instead, which is the mirror case.