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REVISION PROBLEMS FOR FIRST MID-TERM EXAM IN PROJECTION
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Represent a point A. Given that:
1) A is at equal distances from and
2) The distance of A from the origin 0 is 8 cms
3) The point A is above and behind
, .
4) The point A lies on the left hand side of at a distance 6 cms
3π
π1
π1 2
π
π2
y = z
A A
2A
2A
2A zyx = 8
z is positive and y is negativeAA
x = -- 6A
8
L
M
A1 =A2 A3
//
Ay
Az
//
Ay Az
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45
//
45
//
KX = - 6
= AA
x 12
z
y
O
2A
2A
2A zyx
2A
2A zy
, Y is -ve , and Z is +ve
y is -ve
A1 = A2
A
A
.
MISSING PROJECTIONS OF POINTS
A = A
A A
1
1
1
2
2
2
3
3
3
A = A
Given A and A .Find A 222
3
//
//
//
//
+
A
A
y
y
1
//
//
y
y
AA
A
AA
A
A
y
y
Given A and A . Find A 11 33
Given A and A . Find A
x
x x12
12
12 ooo
zzz
+
++
+
+ +
A
AA 23
1
O
//
//
+
+
+
//
////
O
B
BB
11
2
2 3
CC
C
//
3
FIND THE MISSING PROJECTIONS
Ox
x
x12
12
12
z
z
z
y
y
y
y
y
y
A
A
B
B
C
C
Given A and A
Given C and C
Given B and B
2 3
2 3
1 2
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m1
m3
m2
x12
o
y
z
C1
C3 C2
A point C m
C m
11
C m 22
C m 33
d(A,x-axis) = 4 cms .Find the locus of A
d(A,y-axis) = 4 cms. Find the locus of A
4 cms
o
Locus of A
Locus of ALocus of A3
4 cms
4 cms
d(A,z-axis) = 4 cms. Find the locus of A
o
o
2
1
3
z
1x
xx 12
12
12
z
2z
Given the two projections of a str. Line m . Represent the following points lying on m : i) A ( 9 ,?,?) ii) B(?, -1.5,?) iii) C(?,?,2.0) iv) D if d ( D,z-axis) = 5.5 cms v) E if d( E, y-axis) = 4 cms
EXAMPLE (3)
1.5
cms
2.0
cms
4 cms
O
5 .5 c
ms
A
A
B
B
C
C
D
DE
E
9 cms
m
m
1
1
1
1
1
122
2
2
22
x12
.
.
Locus of D1
Locus of E 2
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2π
3π
The points of intersection of a straight line m with the principle planes are called TRACES
The horizontal trace H = m π z = 0
The vertical trace V = m y v = 0
The side trace S = m x s = 0
1
H
3
m 3
m
m1
m2
H2
H=H1
V1
V=V2
S1
S =S3
S2
H
y
z
1
2
3 x
O
V 3
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o
m1
m3m2
x12
y
z
H2
H3
V2V3
S1
S2S3
V1
=
=
= H
V
S
H1
EXAMPLE (5)
m
m
mS
S
S
H
H
H
LOCUS OF A
1
1
1
2
2
2
3
3
3
3
A
AA3
1
2
R= 4
Represent a point A lying on the given str. Line m and d(A,x-axis) = 4 cms
m
m
m
11
2
2
2
3
3
3
x12
V=VV
V H H
1
1
2
S
SS=S3
H=H
45
Find m and the traces of the given str. Line m3
-3 cms
H =H 1
A
A
H1
1
12
2
2
m
m
m
VV = V
2
2
2
V
.
.
B B
B
1
1
O
3
H
3
3
3
.3A
S = S
S
S3
Given m and m .Find i) m ii) the traces H, V and S of m iii) the point A on m if A ( ?, - 3, ?)
iv) The point B on m if B is the closest point to z- axis
1 2 3
/
/
A
B
A
B
B
A B
A
B
A
B
A x
z
y
O
1
3
3
T.L
T. L
A2
B
z
z
BB
B
A
A
A
yy
x
x
π
π
π 2
1
3z
A
A
A
zB
BB
y
yx
x
2
α
β
TRUE LENGTH OF A SEGMENT AB AND ITS INCLINATIONS ON π , i =1,2,3
αβ
T. L
i
1
A3
A1
A2
B1
B3 B2
m1
m 3m
2
x12
o
y
z
yB
yA
T.L[A][B]
yA
yB
zB
zA
T.L[A]
[B]
zA
zB
xA
xB
xA
xB
[A][B] T. L
β
α
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B1
o
Δy
zΔ
Δx
A3
A1
A2
B3
B2
m1
m3
x12
y
z
m2
[B]
β
[A]
[B]
γT.L
T.LT.L
Δx Δy
zΔ
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There are three right angled triangles which are frequently used in solving problems in PROJECTION ;
T. L
Horizontal projection
Δz
T. LΔy
T. L
Side projection
Δx
Vertical projection
Represent the two projections of an equilateral triangle( االضالع متساوى ABC if its (مثلثside AB is given and C(?, 1, ?).
0
X12
B1
A2
A1
B2
1LOCUS OF C1
Locus of c2
Δy
Δy
T. L
of A
B
1Locus of c1
x12
A2
B2
0
B1
A1
ACΔy T. L of BCBCΔy
T. L of AC
Vertical projection. of AC Vertical projection. of BC
.
. C2
C1
Locus of C2
/
/ //
//
T.L. of AB = T.L. of AC = T.L. of BC
ACΔyT. L
of A
C
A C2 2
/
BCΔyT. L of BC
B C 2 2
//
AB
AB