2-grafik ishi.
Mavzu: Berilgan o‘zaro ayqash ikki to‘g‘ri chiziqlar orasidagi eng qisqa masofani proyeksiyalar tekisliklarini almashtirish usulida topish.
Masala. AB(A′B′, A″B″) va CD(C′D′, C″D″) uchrashmas to‘g‘ri chiziq kesmalari orasidagi masofani aniqlansin (1–rasm).
Yechish. Bunda CD kesmaga parallel qilib yangi V1 frontal proyeksiyalar tekisligi o‘tkaziladi. Bu tekislikda CD va AB kesmalarning yangi frontal proyeksiyalari C″1D″1va A″1B″1 lar yasaladi. So‘ngra C″1D″1 kesmaga perpendikulyar qilib N1 tekislik o‘tkaziladi. Bu tekislikda C″1D″1va A″1 B″1 larning yangi gorizontal proyeksiyalari topiladi. Bunda CD kesma C′1≡D′1 nuqta ko‘rinishida proyeksiyalanadi. Bu nuqtadan A′1 B′1 kesmaga tushirilgan E′1 F′1 kesmaning uzunligi CD va AB lar orasidagi masofa bo‘ladi. Teskari proyeksiyalash bilan E va F nuqtalarning E′, E″ va F′, F″ proyeksiyalari yasalgan.
1-rasm.
Yuqoridagi masalani, birinchidan, V1 tekislikni AB kesmaga parallel va H1 tekislikni uning yangi proyeksiyasiga perpendikulyar qilib o‘tkazib yechsa, ikkinchidan esa AB yoki CD kesmalardan biriga parallel qilib avval H tekislikni, so‘ngra ularning proyeksiyalaridan biriga perpendikulyar qilib V ni almashtirsa ham bo‘ladi.
Topshiriqni bajarish uchun variantlar
№
|
А
|
B
|
C
|
D
|
E
|
F
|
S
|
X
|
Y
|
Z
|
X
|
Y
|
Z
|
X
|
Y
|
Z
|
X
|
Y
|
Z
|
X
|
Y
|
Z
|
X
|
Y
|
Z
|
X
|
Y
|
Z
|
1
|
110
|
85
|
50
|
25
|
45
|
5
|
90
|
5
|
105
|
130
|
50
|
55
|
60
|
90
|
10
|
10
|
10
|
90
|
100
|
25
|
20
|
2
|
105
|
90
|
55
|
15
|
50
|
15
|
85
|
15
|
95
|
105
|
30
|
45
|
50
|
100
|
5
|
10
|
5
|
80
|
30
|
90
|
100
|
3
|
110
|
10
|
55
|
85
|
80
|
5
|
30
|
40
|
100
|
130
|
30
|
60
|
10
|
90
|
10
|
60
|
5
|
100
|
45
|
10
|
25
|
4
|
10
|
100
|
30
|
40
|
40
|
100
|
115
|
55
|
5
|
25
|
50
|
15
|
65
|
5
|
75
|
100
|
100
|
40
|
25
|
30
|
10
|
5
|
115
|
95
|
85
|
95
|
25
|
5
|
10
|
5
|
50
|
40
|
95
|
5
|
10
|
35
|
65
|
115
|
15
|
35
|
60
|
85
|
10
|
6
|
90
|
90
|
80
|
65
|
10
|
10
|
10
|
20
|
65
|
110
|
30
|
35
|
35
|
70
|
100
|
15
|
15
|
20
|
35
|
65
|
10
|
7
|
110
|
90
|
90
|
95
|
0
|
20
|
10
|
65
|
45
|
55
|
5
|
110
|
115
|
50
|
80
|
25
|
85
|
0
|
70
|
90
|
10
|
8
|
100
|
5
|
35
|
10
|
30
|
95
|
30
|
100
|
5
|
120
|
95
|
10
|
10
|
65
|
35
|
60
|
5
|
70
|
80
|
70
|
70
|
9
|
100
|
25
|
15
|
65
|
85
|
90
|
20
|
10
|
55
|
120
|
50
|
60
|
10
|
70
|
105
|
40
|
5
|
10
|
45
|
75
|
15
|
10
|
115
|
30
|
10
|
80
|
90
|
95
|
10
|
10
|
60
|
120
|
15
|
70
|
20
|
35
|
90
|
60
|
85
|
15
|
40
|
85
|
25
|
11
|
80
|
5
|
85
|
10
|
85
|
40
|
125
|
60
|
5
|
130
|
25
|
20
|
20
|
35
|
90
|
80
|
105
|
5
|
40
|
20
|
10
|
12
|
110
|
40
|
90
|
85
|
100
|
20
|
30
|
15
|
60
|
130
|
45
|
70
|
10
|
95
|
10
|
60
|
5
|
95
|
110
|
10
|
20
|
13
|
110
|
60
|
10
|
25
|
110
|
50
|
90
|
5
|
90
|
130
|
55
|
45
|
60
|
100
|
5
|
10
|
20
|
85
|
45
|
35
|
20
|
14
|
15
|
30
|
10
|
50
|
90
|
95
|
120
|
10
|
50
|
10
|
15
|
70
|
110
|
35
|
90
|
70
|
85
|
15
|
100
|
85
|
15
|
15
|
115
|
65
|
90
|
75
|
5
|
5
|
10
|
90
|
40
|
120
|
80
|
30
|
15
|
65
|
10
|
55
|
10
|
85
|
30
|
25
|
80
|
16
|
30
|
80
|
90
|
55
|
10
|
10
|
110
|
65
|
30
|
10
|
35
|
30
|
85
|
100
|
70
|
105
|
20
|
15
|
85
|
15
|
65
|
17
|
10
|
85
|
95
|
30
|
5
|
25
|
115
|
50
|
5
|
85
|
5
|
95
|
115
|
65
|
35
|
10
|
35
|
15
|
65
|
10
|
85
|
18
|
115
|
30
|
100
|
85
|
100
|
40
|
10
|
5
|
55
|
100
|
15
|
50
|
80
|
75
|
5
|
25
|
40
|
100
|
100
|
10
|
30
|
19
|
10
|
55
|
90
|
100
|
15
|
50
|
30
|
95
|
15
|
10
|
45
|
30
|
65
|
5
|
100
|
105
|
80
|
5
|
85
|
100
|
90
|
20
|
30
|
65
|
10
|
55
|
5
|
80
|
110
|
90
|
40
|
10
|
60
|
30
|
130
|
10
|
90
|
80
|
100
|
5
|
95
|
25
|
10
|
21
|
21
|
50
|
85
|
115
|
5
|
45
|
50
|
105
|
5
|
10
|
55
|
50
|
80
|
10
|
90
|
130
|
90
|
10
|
40
|
10
|
25
|
22
|
15
|
90
|
65
|
55
|
5
|
5
|
120
|
40
|
90
|
10
|
30
|
80
|
115
|
10
|
65
|
75
|
85
|
10
|
100
|
80
|
25
|
23
|
30
|
90
|
40
|
55
|
20
|
100
|
110
|
60
|
15
|
100
|
70
|
45
|
30
|
10
|
95
|
80
|
95
|
5
|
30
|
20
|
10
|
24
|
30
|
10
|
60
|
115
|
50
|
110
|
50
|
90
|
5
|
10
|
45
|
55
|
80
|
5
|
10
|
130
|
85
|
20
|
95
|
20
|
35
|
25
|
115
|
10
|
30
|
80
|
95
|
90
|
10
|
50
|
10
|
120
|
70
|
15
|
20
|
90
|
35
|
60
|
15
|
85
|
30
|
15
|
85
|
26
|
60
|
85
|
5
|
130
|
40
|
85
|
15
|
5
|
60
|
10
|
20
|
25
|
120
|
90
|
35
|
90
|
5
|
105
|
100
|
10
|
20
|
27
|
30
|
35
|
5
|
120
|
95
|
30
|
100
|
5
|
100
|
10
|
10
|
95
|
120
|
35
|
65
|
70
|
70
|
5
|
50
|
70
|
70
|
28
|
15
|
95
|
95
|
30
|
25
|
5
|
115
|
50
|
70
|
70
|
115
|
10
|
10
|
85
|
55
|
100
|
5
|
90
|
65
|
15
|
95
|
29
|
15
|
10
|
30
|
50
|
95
|
90
|
120
|
60
|
10
|
10
|
70
|
15
|
110
|
90
|
35
|
70
|
15
|
85
|
90
|
25
|
85
|
30
|
30
|
15
|
25
|
65
|
90
|
85
|
110
|
55
|
10
|
10
|
60
|
50
|
120
|
105
|
70
|
90
|
10
|
5
|
85
|
15
|
70
|
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