Question

The end projectors of a line AB is 40 mm. The point A is 24 mm above HP and 10 mm in front of VP. Point B is 46 mm above HP and 46 mm in front of VP.  What will be the True length of the line?

(a) 57 mm

(b) 37 mm

(c) 50 mm

(d) 47 mm

This question was addressed to me during an interview.

My doubt is from Projections on Auxiliary Planes topic in section Orthographic Projection, Projections of Lines, Planes and Solids of Civil Engineering Drawing

Answer 1

The correct choice is (a) 57 mm

For explanation I would say: Refer the figure below and the following steps-

• Draw the XY line. Draw two line perpendicular to XY line separated by a horizontal distance of 40 mm.

• Along the first line mark points a’ and a 24 mm above and 10 mm below XY line.

• Along the second line mark b and b’ 46 mm above and below XY line.

• Draw a reference line X1 Y1 parallel to line ab to represent the AVP.

• Through a and b, draw projectors to X1 Y1 line and extend it.

• Mark a2’ such that 3-a2’ = 5-a’. similarly mark b2’ such that 4-b2’ = 6b’.

• Join a2’-b2’ to obtain the true length of the line.

• The inclination of the line a2’-b2’ with X1Y1 line is the true inclination of the line with HP.

• Draw X2Y2 parallel to the front view a’b’ and project the auxiliary top view a1b1 in the similar manner.  The inclination of the line a1-b1 with X2Y2 line is the true inclination of the line with VP.

By measurement, the following dimensions are obtained:

True length of the line is 57 mm.