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1. Projections of Points and Lines
1. Aim
2. Notations
3. Quadrant Theory
5. Projection of a Points
6. Lines - Important Information
7. Simple cases of Lines-Illustration
8. Lines inclined to one Plane - Illustration
9. Simple cases of Lines
10. Problems
11. ILLUSTRATION – Lines inclined to both planes
12. Five problems Group (A)
13. Information Group (B)
14. Traces
15. Problems 7 nos. Group (B)
16. Lines in Auxiliary Planes Group (C) Information
17. Problems Group (C)
4. A point in different Quadrants
18. Application of Lines Information
19. Problems (10 nos.)
20. Lines in Different Quadrants

2. NOTATIONS
FOLLOWING NOTATIONS SHOULD BE FOLLOWED WHILE NAMEING
DIFFERENT VIEWS IN ORTHOGRAPHIC PROJECTIONS.
IT’S FRONT VIEW a’ a’ b’
SAME SYSTEM OF NOTATIONS SHOULD BE FOLLOWED
INCASE NUMBERS, LIKE 1, 2, 3 – ARE USED.
OBJECT POINT A LINE AB
IT’S TOP VIEW a a b
IT’S SIDE VIEW a” a” b”

3. X
Y
1ST Quad.
2nd Quad.
3rd Quad. 4th Quad.
X Y
VP
HP
Observer
THIS QUADRANT PATTERN,
IF OBSERVED ALONG X-Y LINE ( IN RED ARROW DIRECTION)
WILL EXACTLY APPEAR AS SHOWN ON RIGHT SIDE AND HENCE,
IT IS FURTHER USED TO UNDERSTAND ILLUSTRATION PROPERLLY.

4. HP
VP
a’
a
A
POINT A IN
1ST QUADRANT
OBSERVER
VP
HP
POINT A IN
2ND QUADRANT
OBSERVER
a’
a
A
OBSERVER
a
a’
POINT A IN
3RD QUADRANT
HP
VP
A
OBSERVER
a
a’
POINT A IN
4TH QUADRANT
HP
VP
A
Point A is
Placed In
different
quadrants
and it’s Fv & Tv
are brought in
same plane for
Observer to see
clearly.
Fv is visible as
it is a view on
VP. But as Tv is
is a view on Hp,
it is rotated
downward 900,
In clockwise
direction.The
In front part of
Hp comes below
xy line and the
part behind Vp
comes above.
Observe and
note the
process.

5. A
a
a’
A
a
a’
A
a
a’
X
Y
X
Y
X
Y
For Tv
For Tv
For Tv
POINT A ABOVE HP
& INFRONT OF VP
POINT A IN HP
& INFRONT OF VP
POINT A ABOVE HP
& IN VP
PROJECTIONS OF A POINT IN FIRST QUADRANT.
PICTORIAL
PRESENTATION
PICTORIAL
PRESENTATION
ORTHOGRAPHIC PRESENTATIONS
OF ALL ABOVE CASES.
X Y
a
a’
VP
HP
X Y
a’
VP
HP
a X Y
a
VP
HP
a’
Fv above xy,
Tv below xy.
Fv above xy,
Tv on xy.
Fv on xy,
Tv below xy.

6. A) SIMPLE CASES OF THE LINE
1. A VERTICAL LINE ( LINE PERPENDICULAR TO HP & // TO VP)
2. LINE PARALLEL TO BOTH HP & VP.
3. LINE INCLINED TO HP & PARALLEL TO VP.
4. LINE INCLINED TO VP & PARALLEL TO HP.
B) LINE INCLINED TO BOTH HP & VP.
STUDY ILLUSTRATIONS GIVEN ON NEXT PAGE
SHOWING CLEARLY THE NATURE OF FV & TV
OF LINES LISTED ABOVE AND NOTE RESULTS.
PROJECTIONS OF STRAIGHT LINES.
INFORMATION REGARDING A LINE means
IT’S LENGTH,
POSITION OF IT’S ENDS WITH HP & VP
IT’S INCLINATIONS WITH HP & VP WILL BE GIVEN.
AIM:- TO DRAW IT’S PROJECTIONS - MEANS FV & TV.

7. X
Y
X
Y
b’
a’
b
a
a b
a’
b’
B
A
TV
FV
A
B
X Y
H.P.
V.P.
a’
b’
a b
Fv
Tv
X Y
H.P.
V.P.
a b
a’ b’
Fv
Tv
For Tv
For Tv
Note:
Fv is a vertical line
Showing True Length
&
Tv is a point.
Note:
Fv & Tv both are
// to xy
&
both show T. L.
1.
2.
A Line
perpendicular
to Hp
&
// to Vp
A Line
// to Hp
&
// to Vp
Orthographic Pattern
Orthographic Pattern
(Pictorial Presentation)
(Pictorial Presentation)

8. A Line inclined to Hp
and
parallel to Vp
(Pictorial presentation)
X
Y
A
B
b’
a’
b
a


A Line inclined to Vp
and
parallel to Hp
(Pictorial presentation)
Ø
a b
a’
b’
B
A
Ø
X Y
H.P.
V.P.
T.V.
a b
a’
b’

X Y
H.P.
V.P.
Ø
a
b
a’ b’
Tv
Fv
Tv inclined to xy
Fv parallel to xy.
3.
4.
Fv inclined to xy
Tv parallel to xy.
Orthographic Projections

9. PROBLEMS ON
SIMPLE CASES OF THE LINES
&
LINES INCLINED TO ONE PLANE,
PARALLEL TO OTHER PLANE.

10. a’
b’
ab
x y
a’
b’
x y
FV
TV
PROBLEM 1.
Line AB, 60 mm long, is perpendicular to Hp and parallel to Vp.
Draw it’s projections if end A is on HP and 30 mm in front of Vp
while end B is above Hp.
ab
TV
FV
PROBLEM 2.
If in previous case end A of line AB is 20 mm
above Hp, draw it’s projections.
30 30
25
60 mm (TL)
60 mm (TL)

11. x y
a’ b’
a b
FV
TV
PROBLEM 3.
Line AB, 60 mm long, is parallel to HP and VP both.
It is 15 mm above Hp and 25 mm in front of Vp.
Draw it’s projections.
25
15
60
Line is in 1st Quadrant
Fv above xy & Tv below xy line.

12. x y
a’ b’
a b
FV
TV
PROBLEM 4.
Line AB, 60 mm long, is parallel to HP and VP both.
It is 15 mm above Hp and 30 mm behind Vp.
Draw it’s projections and state the quadrant in which it is lying.
15
30
60
Line is in 2nd Quadrant
Fv & Tv both are above xy line.

13. x y
a’ b’
a b
FV
TV
PROBLEM 5.
Line AB, 60 mm long, is parallel to HP and VP both.
The line is in Hp and 25 mm in front of Vp.
Draw it’s projections.
25 mm
60

14. x Y
a’ b’
a b
FV
TV
PROBLEM 6: Line AB, 60 mm long is
contained by both Hp & Vp. Draw it’s
projections.
60

15. x y
a’
b’
a b
TV
Problem 7 : Line AB, 70 mm long and 400 inclined
to Hp is parallel and 25 mm in front of Vp. If end A is
15 mm above Hp, draw it’s projections.
15
25
Line is in 1st Quadrant
Fv above xy & Tv below xy line.

16. x y
a’ b’
a
b
Ø
FV
Problem 8 : Line AB, 70 mm long is inclined to Vp &
is in Hp. If end A is 15 mm in front of Vp & it’s Fv
measures 50 mm in length, draw it’s projections and
find it’s inclination with Vp.
50
15
Answer
Ø = Inclination with Vp
Line may be in 1st or 4th
Quadrant as Fv on xy
but Tv is below xy line.

17. x y
a’ b’
a
b
Ø (400)
FV
Problem 9 : Line AB, 70 mm long and 400 inclined
to Vp is parallel and 25 mm below Hp. If end A is 15
mm behind Vp, draw it’s projections.
15
25
Line is in 3rd Quadrant
Fv below xy & Tv above xy line.

18. x y
a’
b’
a b
Answer: Fv is TL
TV
Problem 10 : Line AB is 400 inclined to Hp is
parallel and 25 mm in front of Vp. It’s Tv measures
50 mm. If end A is in Hp and 25 mm in front of Vp,
draw it’s projections & find True Length of line AB.
50
25
Line is in 1st Quadrant
Fv above xy & Tv below xy line.

19. x y
a’
b’
a b
TV
Problem 11 : Line AB, 70 mm long and 400 inclined
to Hp is lying in Vp. If end A is in Hp, draw it’s
projections. Consider end B above Hp.
Line may be in 1st or 2nd
Quadrant as Fv is above xy
and Tv on xy line.

20. x y
a’
b’
a b
TV
Problem 12 : Line AB, 70 mm long and 400
inclined to Hp. It is parallel and 25 mm behind
Vp. If end A is 15 mm above Hp,draw it’s
projections.
15
25
Line is in 2nd Quadrant
as Fv and Tv both are
above xy line.

21. a’
b’
a b
Answer:
Fv = True Length
TV
Problem 13 : Line AB, 400 inclined to Hp is parallel and 25
mm in front of Vp. End A is 40mm below Hp. If it’s Tv is 50
mm long, draw it’s projections and find it’s True Length.
15
25
50
x y
Line is in 4th Quadrant
as Fv and Tv both are
below xy line.