Download - 3 Dimension (Distance)
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3 Dimension(Distance)
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BASE COMPETENCE :
Determine distance between two points, a point to line and a point to
plane in the 3 dimension.
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THE MATERIAL
Distance in 3 Dimension : distance between two points
distance point to line
distance point to plane
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Distance between two points
Distance from points A to
point B is the shortest way
from A to B
A
B
Distan
ce b
etwee
n tw
o po
ints
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Example 1Given :The cube ABCD –EFGHWith the long of the edge is a cm.
Find distance : 1. point A to C, 2. Point A to G,3. Point A to centre of line FH
A BCD
HE F
G
a cm
a cm
a cm
P
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Solving: Look at the right
triangle ABC
that right at B, so
AC = = = = So distance A to C= cm(AC is side diagonal)
A BCD
HE F
G
a cm
a cm
a cm
22 BCAB 22 aa
2a2
2a
2a
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Distance A to G = ?Look at the triangle
ACG thatright at C, so
AG =
= = = =So distance A to G = cm(AG is space diagonal)
A BCD
HE F
G
a cm
a cm
a cm
22 CGAC 22 a)2a(
2a3 3a
3a
22 aa2
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A BCD
HE F
G
a cm
P
Distance A to P = ?Look at the triangle
AEP thatRight at E, so
AP =
=
=
= =So distance A to P = cm
22 EPAE
2
212 2aa
2212 aa
223 a 6a2
1
6a21
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Distance point to line
A
g
Dis
tanc
e fr
om p
oint
A
to li
ne g
Distance point A to line g is length of perpendicular segment from point A to line g
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Example 1
Given cubeABCD-EFGH, with length of edge5 cm.Distance point A to segment HG is….
A BCD
HE F
G
5 cm
5 cm
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Solving
Distance point A tosegment HG is segment AH, (AH HG)
A BCD
HE F
G
5 cm
5 cm
AH = (AH side diagonal)
AH =
So distance A to HG = 5√2 cm
2a
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Example 2
Given cubeABCD-EFGHWith length of edge 6 cm.Distance point B to diagonal AG is….
A BCD
HE F
G
6 cm
6 cm
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Solving
Distance B to AG =Distance B to P (BPAG)Side diagonal BG =6√2 cmSpace diagonal AG= 6√3 cmLook at triangle ABG
A BCD
HE F
G
6√2
cm6 cm
P6√
3 cm
A B
G
P
6√3
6
6√2
?
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Look at the triangle ABGSin A = = =
BP =
BP = 2√6
A B
G
P6√
3
6
6√2AG
BGAB
BP
36
26
6
BP
36
)6)(26(
?
So distance B to AG = 2√6 cm
3
66
3
3x
2
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Example 3
Given T.ABCDUniform pyramid.Length of the based side is 12 cm, and Length of the vertical side is 12√2 cm. Distance A to TC is…12 cm
12√2
cm
T
C
A B
D
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Solving
Distance A to TC = APAC = side diagonal = 12√2AP = = = =
So distance A to TC = 6√6 cm
12 cm
12√2
cm
T
C
A B
D
P
12√2
6√2
6√2
22 PCAC 22 )26()212( 108.2)36 144(2
6636.3.2
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Example 4
Given cubeABCD-EFGHWith length of edge6 cmA B
CD
HE F
G
6 cm6 cm
point P at the middle of FG.
Distance point A to line DP is….
P
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A BCD
HE F
G
6 cm6 cm
P
Solving
Q
6√2
cm
R
P
AD
G F
6 cm
3 cm
DP =
=
=
22 GPDG 22 3)26(
9972
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Solving
Q
6√2
cm
R
P
AD
G F
6 cm
3 cmDP =
Area of triangle ADP
½DP.AQ = ½DA.PR
9.AQ = 6.6√2
AQ = 4√2
So distance A to DP = 4√2 cm
9972
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Distance point to plane
Distance between point A to plane V is length of segment that connect perpendicular point A to plane V
A
V
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Line perpendicular Plane
Line g said perpendicular plane V if line g perpendicular at two lines that intersection in plane V
V
g
a
bg a, g b,
So g V
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Example 1
Given cubeABCD-EFGHWith edge length 10 cmDistance point A toplane BDHF is….
A BCD
HE F
G
10 cm
P
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Solving
Distance point A toPlane BDHF Represented by length of line AP. (APBD)AP = ½ AC (ACBD) = ½.10√2 = 5√2
A BCD
HE F
G
10 cm
P
So distance A to BDHF = 5√2 cm
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Example 2
Given uniform pyramid T-ABCD.Length of AB = 8 cmand TA = 12 cm.Distance point T to plane ABCD is…
8 cm
T
C
A B
D
12 c
m
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Solving
Distance T to ABCD = Distance T to intersection AC and BD = TP AC is side diagonal AC = 8√2AP = ½ AC = 4√2
8 cm
T
C
A B
D
12 c
m
P
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AP = ½ AC = 4√2 TP = = = = = 4√7 8 cm
T
C
A B
D
12 c
m
P
2 2 AP AT 2 2 )24( 12
32 144 112
So distance T to ABCD = 4√7 cm
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Example 3
Given cubeABCD-EFGHWith length of edge 9 cm.Distance point C to plane BDG is…
A BCD
HE F
G
9 cm
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Solving
Distance point C to plane BDG = CPCP perpendicular with GT
A BCD
HE F
G
9 cm
PT
CP = ⅓CE = ⅓.9√3 = 3√3
So distance C to BDG = 3√3 cm
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GOOD LUCK !GOOD LUCK !