A straight line AB is 60 mm long. It is inclined to H.P. and V.P. by an angle of 30° and 45° respectively. Point A is 30 mm above H.P. and 20 mm in front of V.P. Draw the projections of straight line AB. Find also the traces.

 Projection of Lines

Question: A straight line AB is 60 mm long. It is inclined to H.P. and V.P. by an angle of 30° and 45° respectively. Point A is 30 mm above H.P. and 20 mm in front of V.P. Draw the projections of straight line AB. Find also the traces.

Given data:

• TL = 60 mm
• θ = 30°
• ɸ = 45°
• a' = 30 mm above HP
• a = 20 mm in front of the VP

Solution:

Procedure:

• Draw an XY line and a vertical line as shown in the figure.
• Project point A according to the given data. (If you don't know the concept of projections of points, click here to learn: Projection of Points)
• The line is inclined to HP by 30° so draw a line from point a' of the length of 60 mm (True length). Name the other endpoint of the line as b1'.
• Now because the line is inclined to VP by 45°, draw a line from the point of 60 mm length. Name the other end of the line as b1. 
• Draw a vertical line from point b1' to the locus of a as shown in the figure. Name that point g.
• Take a compass with a radius of ag and draw an arc to the locus of b.
• At where the arc and locus of b intersect, name that point b.
• Draw the line ab which will be the top view of the line. 
• Measure its length( should be around 53 mm) and inclination( should be around 56°) from the locus of a.
• For the front view of the line, simply draw a vertical line from point b to the locus of b'.
• Where the vertical line and the locus of b' intersect, name that point b'.
• Draw the line a'b' which will be the front view of the line.
• Measure its length( should be around 43 mm) and inclination( should be around 45°) from the locus of a'.
• For the trace, expand the lines ab and a'b' to the locus of a and XY line respectively another side of the vertical line.
• Where the lines intersect with XY line and name them v and h'.
• Draw vertical lines from points v and h'.
• Where the lines intersect with those vertical lines name those points h'T and vT as shown in the figure.
• Your problem is solved.

I hope you understood the question and solution as well. If you have any doubts regarding the solution or questions, just let me know in the comment section! Till then keep learning, and keep improving!

Similar Problems:

1. The elevation of line AB, 80 mm long, measures 55 mm. The end A is 20 mm above H.P. and 10 mm in front of V.P. Draw the projections of the line and find its true inclinations with H.P. and V.P. If the end B is 25 mm below H.P. and is behind V.P.
   
2. Find M of a line MN, which is inclined at 46° to H.P. and 20° to V.P. is 15 mm above the H.P. and it is in front of the V.P., while the end N is 60 mm in front of V.P. and is above H.P. Draw the projections of the line, find its true length if its plan length is 70 mm. Locate the points of intersection of the line with the principal planes.
3. Draw the projections of the following points on the same x-y line. 1) Point A on V.P. and 30 mm below H.P. 2) Point B on H.P. and 20 mm in front of V.P. 3) Point C 20 mm above H.P. and 20 mm behind V.P. 4) Point D 25 mm below H.P. and 40 mm behind V.P. 5) Point E on H.P. and on V.P. 6) Point F 40 mm above H.P. and 10 mm in front of V.P. 7) Point G on V.P. and 35 mm above H.P.