Eg unit 2 1

20MEG01 Engineering Graphics
Module 2
Prepared by:
M. Sundra Pandian, M.E., M.B.A.
Assistant Professor, Department of Mechanical Engineering,
Sri Ramakrishna Institute of Technology, Coimbatore - 10

Syllabus
Projection of Points, Lines and Plane Surfaces
(Module 2)
Projection of points – Projection of straight lines
(only First angle projections) inclined to both the
principal planes – Determination of true lengths and true
inclinations by rotating line method and trapezoidal
method and traces – Projection of planes (polygonal and
circular surfaces) inclined to both the principal planes by
rotating object method.

Introduction
A point may be situated, in space, in any one of the four
quadrants formed by the two principal planes of projection or may
lie in any one or both of them.

Introduction
Its projections are obtained by extending projectors
perpendicular to the planes.
x
y x y
VP
HP
Reference Line

Introduction
Quadrant I
Above HP &
In front of VP
Quadrant II
Above HP &
Behind VP
Quadrant III
Below HP &
Behind VP
Quadrant IV
Below HP
In front of VP
VP
HP

Introduction
A point may be situated, in space, in any one of the four
quadrants formed by the two principal planes of projection or may
lie in any one or both of them.
One of the planes is then rotated so that the first and third
quadrants are opened out.
The projections are shown on a flat surface in their
respective positions either above or below or in xy

Projections of Points
Let the point “A” be on the first quadrant at a height of
„h‟ mm from the ground or Horizontal plane, H.P and at a distance
of „y‟ mm in front of the wall or vertical plane or V.P.
Lets draw the projections of the point A.
It is noted that the point is in
Quadrant 1.
Drawing the perpendicular
projector to the ground from the point
A, the projectors hits the H.P. at the
point a and similarly the V.P at a‟.

Let the point “A” be on the first quadrant at a height of
„h‟ mm ABOVE the ground or Horizontal plane, H.P and at a
distance of „y‟ mm IN FRONT OF the wall or vertical plane or V.P.
• The point will always be denoted in
lowercase letter.
• Elevation or Front view or F.V should
always be indicated with an
apostrophe ( „ ).
• Plan or Top view or T.V should always
be indicated with the lowercase letter
without apostrophe ( „ ).

It can be noted that if a point lies in the 1st quadrant, the
elevation or F.V will always be above the reference line x y and its
plan or top view will always be below the reference line.

Exercise
A point A is 50 mm above the ground and 60 mm in front of V.P.
Draw its projections.
x y
50
a‟
60
a
F.V
T.V
Above HP – Above x y
Below HP – Below x y
In front of VP – Below x y
Behind VP – Above x y
HP dimension – F.V. – Have „
VP dimension – T.V. – No „

Similarly let us consider a point in 3rd quadrant.
The point will be BELOW the H.P and Behind the V.P.

It can be noted that if a point lies in the 3rd quadrant, the
elevation or F.V will always be below the reference line x y and its
plan or top view will always be above the reference line, just the
vice-versa of quadrant 1.

Exercise
A point C is 40 mm below the ground and 30 mm behind V.P. Draw
its projections.
x y
30
c
40
c‟
T.V
F.V
HP dimension – F.V. – Have „
VP dimension – T.V. – No „

Comparison of Projections of Points in Quadrants 1 and 3
Quadrant 1 Quadrant 3
Note:
A point denoted by an alphabet alone is the T.V or plan and the
same alphabet along with an apostrophe ( „ ) is the F.V or elevation.

Let us consider a point in 2nd quadrant.
The point will be ABOVE the H.P and Behind the V.P.

It can be noted that if a point lies in the 2n quadrant, the
elevation or F.V will always be above the reference line x y and its
plan or top view will also be always above the reference line.

Exercise
A point B is 40 mm above the ground and 50 mm behind V.P. Draw
its projections.
x y
40
b‟
50
b
F.V
T.V

Let us consider a point in 4th quadrant.
The point will be BELOW the H.P and IN FRONT OF the V.P.

Exercise
A point D is 50 mm below H.P. and 30 mm in front of V.P. Draw its
projections.
x y
30
d‟
50
d
F.V
T.V

Comparison of Projections of Points in Quadrants 2 and 4
Quadrant 2 Quadrant 4
Note:
A point denoted by an alphabet alone is the T.V or plan and the
same alphabet along with an apostrophe ( „ ) is the F.V or elevation.

q’
1. Draw the projections of the following points.
i. P is 40 mm above HP and 30mm in front of VP.
ii. Q is 30 mm above HP and 40 mm behind VP.
iii. R is 20 mm below HP and 35 mm behind VP.
iv. S is 30 mm below HP and 40 mm in front of VP
P’
Exercise
x y
40
30
P
30
40
q
20
r’
35
r
30
s’
40
s

1. Draw the projections of the following points.
i. A is 50 mm above HP and 40mm behind VP.
ii. B is 35 mm below HP and 50 mm behind VP.
iii. C is 20 mm above HP and 35 mm in front of VP.
iv. D is 40 mm below HP and 50 mm in front of VP.
v. E is 35 mm in front of VP and on HP.
vi. F is on VP and 40 mm above HP.
vii. G is on both HP and VP.
viii. H is 35 mm below HP and on VP.
ix. I is 30 mm behind VP and on HP.
x. J is 40 mm in front of VP and on HP.
Exercise

Line is defined as the connector between two points in space.
If the connector distance is the shortest then, it is the straight line.
Projection of Lines
Point Line
Curve
Compound Line

Like the points is different quadrants, we will discuss about
the lines in different positions and its projections.
The projections will all be in the first quadrant or first angle
projections..
Projection of Lines

The line will either be parallel to Horizontal Plane (H.P) or
Vertical Plane (V.P.) to both planes (H.P & V.P)
The projections will all be in the first quadrant or first angle
projection as shown in the fig. below.
Line is Parallel to one or both planes

The actual or original or true length will always be shown in
the plane to which the line is parallel to.
The True length (T.L) will be the actual length of line which
is always shown only in the plane where the line is parallel.
So if the line is parallel to HP the top view or plan will show
the original length .
If the line is parallel to the VP, the true length will be shown
or can be measured from the front view or elevation.
If the line is parallel to both HP and VP, the true length is
shown in both the Front and Top views.
Line is Parallel to one or both planes

x
y
Reference Line
25
25
1. Draw the projections of a 75 mm long straight line, if it is
parallel to both the H.P. and the V.P. and 25 mm from each.
A
B
Exercise – Line Parallel to both H.P & V.P

1. Draw the projections of a 75 mm long straight line AB, if it is
parallel to both the H.P. and the V.P. and 25 mm from each.
Exercise – Line Parallel to both H.P & V.P
x y
25
a‟
75
b‟
25
a b
25
Note:
Parallel to VP – F.V True Length
Parallel to HP – TV True length
FV
TV

x
y
The line will be lying in either H.P or V.P or both (in the
intersection of both planes i.e., at the reference line x-y).
A B
Exercise – Line contained in one or both planes.
C
D
E
F

x
y
Reference Line
Either the inclination angle will be given or the distance of
each end (e.g. A and B) of the line from the V.P will be given.
A
B
Exercise – Line contained in H.P & Inclined to V.P
ø°
a‟
b‟

1. Draw the projections of an 80 mm long straight line AB, if it is
contained in H.P. and the end A is 25 mm and end B is 50 mm from
V.P.
Exercise – Line in H.P & Inclined to V.P
x y
25
a
b
a‟ b‟
T. L = 80
P. L = ?
50

30°
contained in H.P. The point A is 25 mm in front of V.P. and the line
is inclined at 30° to V.P.
Exercise – Line in H.P & Inclined to V.P
x y
25
a
T. L = 80
b
a‟ b‟
P. L = ?

x
y
Reference Line
A
B
Exercise – Line contained in V.P & Inclined to H.P
°

d‟
1. Draw the projections of a 70 mm long straight line CD, if it is
contained in V.P. and the end A is 30 mm and end B is 60 mm above
H.P.
Exercise – Line in V.P & Inclined to H.P
x y
30
c‟
60
c d
T. L = 70
P. L = ?

1. Draw the projections of a 60 mm long straight line CD, if it is
contained in V.P. The point C is 30 mm above H.P. and the line is
inclined at 45° to H.P.
45°
Exercise – Line in V.P & Inclined to H.P
x y
30
a
T. L = 60
b
a‟
b‟
P. L = ?

x
y
d
E
F
Exercise – Line Parallel to H.P & Perpendicular to V.P
ø°

parallel to H.P. and inclined to V.P. at 30°. The point A is 20 mm
above HP and 30mm in front of VP.
Exercise – Line Parallel to one plane & incline to another
x y
30
a 30°
T. L = 50
b
20
a‟
b‟
P. L = ?
T. L = 50

x
y
Reference Line
25
25
The projection will be true length will be shown in the plane
where the line is parallel.
The projection of the line will be a point in the plane where
it is perpendicular.
A
B
Line Parallel to one plane & Perpendicular to another
x
y
25
25
A
B

Line Parallel to one plane & Perpendicular to another
Case 1:-
The line is parallel to HP
and perpendicular to VP.
x y
a
b
Case 2:-
The line is parallel to VP
and perpendicular to HP.
x y
a‟
b‟
a‟ (b‟)
a (b)

E.g: The top view of a line, parallel to V.P and inclined 45 ° to the
H.P is 50 mm. One end of the line is 20 mm above H.P and 30
mm in front of V.P. Draw the projections and find the true
length of the line.
In these kind of problems, the location of the points, angle of
inclination and the projected length will be given and the true
length of the line will be required.
So the projected length is drawn and the true or original
length of the line will be derived from it in the reverse drawing
method as followed in the previous problems.
Exercise – To find the True Length (T.L)

45°
a
a‟
Exercise – Finding the True Length (T.L.)
x y
20
30
b
b‟
50
T.L. = ….

a
1. The front view of a 75 mm long line measures 55 mm. The
line is parallel to H.P and one end is in V.P. and 25 mm above
H.P. Draw the projections of the line and its inclination to V.P.
Exercise – To find the True Length (T.L) & Inclination
x y
25
a‟ 55 b‟
R = T.L. = 75
b
Ø = …

Line Inclined to both planes
In this case the line will be inclined to H.P at an angle of
„‟ and inclined to V.P at an angle of „ø‟.
So the true length can be readily available in any plane to
project to the other plane.
A
B
ø °
° H.P
Inclination
V.P
Inclination

1. Draw the projections of a 80 mm long straight line GH, if it is
inclined at 45° to H.P. and 30° to V.P. The point G is 15 mm above
HP and 20 mm in front of V.P.
Hint: H.P Dimension & angle – Above x-y
V.P Dimension & angle – Below x-y
Whenever a line is inclined to a plane, the
true length can‟t be measured from the projections.
Exercise – Line Inclined to Both Planes

(Given angle of Inclinations , ø and Position of one end)
x y
15
a‟
1. Draw the projections of a 80 mm long straight line, if it is
inclined at 45° to H.P. and 30° to V.P. One end is 15 mm above HP
and 20 mm in front of V.P.
Method:
• First assume the line is inclined to H.P. and parallel to V.P.
Draw the front view. Then assume the line is inclined to
V.P. and parallel to H.P.
• Then the original length of the line will be projected in
the front view.
45°
b‟

45°
(Given angle of Inclinations , ø and Position of one end)
x y
15
a‟
b‟
20
Path or
Locus of a‟
Path or
Locus of b‟
a 30°
b
Path or
Locus of a
Path or
Locus of b
b1
b1‟
b2‟
 = …
b2
 = …

(Given Positions of both ends
To find the angle of inclinations )
1. Draw the projections of a 70 mm long straight line, having its
left end 20 mm above H.P. and 25 mm in front of V.P. and the right
end is 40 mm above the H.P. and 50 mm in front of V.P. Draw the
projections and find the inclinations of the line.
Method:
• First assume the line is inclined to H.P. and parallel to V.P.
Draw the front view. Then assume the line is inclined to
V.P. and parallel to H.P.
• Then the original or true inclinations of the line will be
determined in the reverse method as used in the previous
problem.
• When the lines are extended they meet the H.P and or the
V.P. This extended meeting point is called the trace

b2
(Given Position of both ends
To find angle of Inclinations  and ø)
x y
20
a‟
Path of a‟
25
Path of a
a
40
Path of b‟
R = T.L. = 70
b‟
50
Path of b
b
b1
b1‟‟
R = T.L. = 70
b2‟‟
° = …
° = …
ø° = …
° = …

Projection of Surfaces
Planes are 2 dimensional figures having only length and
width and no thickness.

Planes Perpendicular to both HP & VP
x
y
A
B
C
D
b‟
c‟
(a‟)
(d‟)
d
c
(a)
(b)

Ex. Draw the projections of a square plane of 30 mm side when
it is perpendicular to both the planes. The plane is 20 mm above
HP and 15 mm in front of VP.
b‟ (a‟)
Planes Perpendicular to both planes
x y
x
y
A
B
C
D
b‟
c‟
(a‟)
(d‟)
d
c
(a)
(b
)
20
30
c‟ (d‟)
15
d (a)
c (b)

Planes Parallel to one plane and
Perpendicular to another
x
y
A
B
C
D
b‟
c‟
(a‟)
(d‟)
d
c
a
b

a
Ex. Draw the projections of a rectangular plane 40 mm X 30
mm when it is parallel to HP and perpendicular to VP. The
plane is 20 mm above HP and 30 mm in front of VP.
Planes Perpendicular to both planes
x y
20
x
y
A
B
C
D
b
‟
c
‟
(a
‟)
(d
‟)
d
c
a
b
b‟ (a‟) c‟ (d‟)
40
30
b c
d
30

x
y
A
B
C
D
a
b
a‟
b‟
c‟
d‟

a‟
Ex. Draw the projections of a square plane of 25 mm side when
it is parallel to VP and perpendicular to HP. The plane is 20
mm above HP and 30 mm in front of VP.
x y
20
d (a) c (b)
25
30
b‟
c‟
d‟
25

Planes Perpendicular to one plane and
Inclined to another
x
y
A
B
C
D
d (a)
c (b)
a‟
b‟
c‟
d‟
HT
VT
Ø °

Inclined to another

Ex. A regular pentagon of 30 mm side has one side on the
ground. Its plane is inclined at 45° to the HP and
perpendicular to the VP. Draw its projection and show its traces
Inclined to another
A
B
C
D
E
Note: When the information of
a side of the polygon is
mentioned, start drawing with
a Vertical line.
If the information given is
about one corner of the polygon
, draw the polygon with a
horizontal line.

A
B
72°
72°
C
D
E
72°
30
30
30
30
72°
30
Drawing a Pentagon

45°
a1
Ex. A regular pentagon of 30 mm side has one side on the
ground. Its plane is inclined at 45° to the HP and
perpendicular to the VP. Draw its projection and show its
traces.
x y
a
b
c
d
e
a‟ (e‟) b‟ (d‟) c‟ a1‟ (e1‟)
c1‟
b1‟ (d1‟)
b1
c1
d1
e1
HT
VT
Note: Imagine the pentagon is parallel / contained in HP.

A
B
60° 60°
60°
60°
90° 90°
30
30
30
30
30
C
D
E
F
Drawing a Hexagon
• Ex. A regular hexagon of 30 mm side has one corner touching
the VP. Its plane is inclined at 30° to the VP and
perpendicular to the HP. Draw its projection and show its
traces.

d1(b1)
Ex. A regular hexagon of 30 mm side has one corner touching
the VP. Its plane is inclined at 30° to the VP and
perpendicular to the HP. Draw its projection and show its
traces.
x y
a‟ b‟
c‟
d‟
e‟
f‟
e(a) d(b) c
f 30°
e1(a1)
c1
f1
a1‟ b1‟
c1‟
d1‟
e1‟
f1‟

30°
Ex. Draw the projections of a 60 mm diameter circle resting on
the HP on one of point on its circumference. The diameter
containing that point is inclined at 45° to HP and 30° to VP.
x y
b
a
c
d
e
f
g
h
a‟ b‟(h‟)c‟(g‟) d‟(f‟) e‟ 45°
a1‟
e1‟
c1‟
b1‟
d1‟
b1
a1
c1
d1
e1
f1
g1
h1
1
2
3
4
5
6

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