Problem 4.10 Projection of Straight Lines – A line AB is 80mm long and the end A is 15mm above H.P. The other end B is 10mm in front of V.P. The line is inclined at 30° with H.P. and 45° with V.P. Draw the projections of the line when it is in 1st quadrant.

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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 a’ at the distance 15mm above the x-y line. And draw a horizontal line from the point a’. This is locus of the point a’. Then from the point a’ draw a line of the length equal to its true length, which is 80mm at an angle 30° with the x-y line. The end point of this line is marked as b1’.This is true length of the line in front view and its inclination with the x-y line is represented by the letter Ɵ. And draw a horizontal line passing through the point b1’which is locus of the point b1’.

* Step-3* Draw a horizontal line at the distance 10mm below the x-y line which is locus of the point b2. And mark a point b2 on this line such that the line form the point b2should incline at the angle 45° with this line, should be of the length 80mm and should intersect on the projector coming downward direction from the point a’. At the point of intersection of this line with the projector give the name of that point as a. This line ab2 is true length of the line in top view. Its inclination with the x-y line is represented by the letter ø. And form the point a draw a horizontal line of some suitable length, this is locus of the point a.

* Step-4* From the point b1’draw a vertical downward projector up to the locus of the point a, and then point a as center and radius equal to the point of intersection of the previously drawn projector, draw an arc which should intersect on the line which is locus of the point b2. And give the notation of that point as b. Then connect the point a and b with a straight line. This is plan of the line AB. Its inclination with the x-y line is represented by the letter β.

* Step-5* From the point b draw a vertical upward projector up to the line which is locus of the point b1’, and mark that point as b’. Then connect the point a’ & b’ with a straight line. This is elevation of the line AB. Its inclination with the x-y line is represented by the letter α.

* Step-6* 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 AB as shown into the figure.