Problem 4.9 Projection of Straight Lines – A line PQ contains a point O on it such that the ratio of the distance of the PO: OQ is 1:2. The end P is 20 mm above H.P. and it is in 1^{st} quadrant. And the other end Q is in V.P. The point O is 35 mm above H.P. The line is inclined with the H.P. at an angle 30°. The elevation length of the line PQ is 70 mm. Draw the projections of the line PQ.

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*Procedure:*

* Step-1 *Draw a horizontal line, which is x-y line of some suitable length.

**Step-2*** *Mark a point p’ at the distance 20 mm above the x-y line.And draw a horizontal line at the distance 35 mm above the x-y line.Then from the point p’ draw a line at an angle 30° with the x-y line such that it should intersect the previously drawn horizontal line at the distance 35 mm and mark that point as o’

_{1}.And measure the distance between p’ – o’

_{1}, which is 30 mm.The ratio of the points

*PO: OQ*is 1:2.So extend the line p’ – o’

_{1 }up to the distance 60 mm, hence the total length of the line p’-q’

_{1 }is 90 mm. This is true length of the line in front view and its inclination with the x-y line is represented by the letter Ɵ.

** Step-3** From the point q’

_{1}draw a horizontal line parallel to x-y line. This is the locus of the point q’

_{1}. Now form the point p’ draw a line such that its length should be equal to 70 mm and it should intersect the line passing through the point q’

_{1}. Give the name of that point as q’. This is elevation of the line PQ. And its inclination with the x-y line is represented by the letter α.

**Step-4*** *From the point q’, draw a downward projector up to the x-y line. And give that point name as q.

**Step-5*** *Now qs’1 as center and p’ as radius draw an arc such that it should intersect with the horizontal line passing through the point q’

_{1}. And give the name of that point as p

_{1}’. From p

_{1}’ draw a vertical downward projector below the x-y line of some suitable length.

* Step-6* From the previously marked point q, draw a line of length equal to 90 mm which should intersect with the vertical downward projector form the point p

_{1}’. And give the name of that point as p

_{2}. It is true length of the line in top view. Its inclination with the x-y line is represented by the letter ø. And from the point p

_{2}draw a horizontal line of suitable length. This is locus of the point p

_{2}.

__Step-7__ Now draw a downward projector form the point p’ up to the line which is locus of the point p2. And give the name of that point as q. Then draw a line between the point p & q. This is plan of the line PQ. Its inclination with the x-y line is represented by the letter β.

* Step-8* Give the dimensions by any one method of dimensions and give the notations as shown into the figure. And make a list of the True Length & Angles made by the line PQ as shown into the figure.