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Transcript of 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance...
![Page 1: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/1.jpg)
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Three Dimension
(Distance)After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension
![Page 2: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/2.jpg)
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We will study the distance :
point to point
point to line
point to plane
line to line
line to plane, and
plane to plane
![Page 3: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/3.jpg)
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The distance of point to point
This display, shows that the
distance of point A to B is the length
of line segment which connect
point A to point B A
B
Jara
k du
a tit
ik
![Page 4: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/4.jpg)
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e. g. :Given that the edge
length of a cube ABCD.EFGH is a cm.
Determine the distance of :
a) Point A to point Cb) Point A to point G
c) The distance of point A to
the middle of plane EFGH
A BCD
HE F
G
a cm
a cm
a cm
P
![Page 5: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/5.jpg)
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Solution:
Consider Δ ABC which has right angle at B
AC = = =
= Thus, the diagonal of AC = cm
A BCD
HE F
G
a cm
a cm
a cm
22 BCAB 22 aa
22a
2a
2a
![Page 6: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/6.jpg)
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Distance of AG
Consider Δ ACG which has right angle at C
AG = = = = =
Thus, the diagonal of AG = cm
A BCD
HE F
G
a cm
a cm
a cm
22 CGAC 22 a)2a(
2a3 3a
3a
22 aa2
![Page 7: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/7.jpg)
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A BCD
HE F
G
a cm
P
Distance of AP
Consider Δ AEP which has right angle at E
AP =
=
=
= =
Thus distance of A to P = cm
22 EPAE
2
212 2aa
2212 aa
223 a 6a2
1
6a21
![Page 8: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/8.jpg)
88
Distance Point to Line
A
g
dist
ance
poi
nt to
line
This display shows the distance from point A to line g is length of the line segment which is connected from point A and is perpendicular to line g.
![Page 9: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/9.jpg)
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e.g. 1:
Given that the edge length of a cube ABCD.EFGH is 5 cm.The distance from point A to the edge of HG is…
A BCD
HE F
G
5 cm
5 cm
![Page 10: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/10.jpg)
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SolutioThe distance from point A to the edge of HG is length of the line segment AH, (AH HG)
A BCD
HE F
G
5 cm
5 cm
AH = (AH is a side diagonal)
AH = Thus, the distance from point A to the edge of HG= 5√2 cm
2a
25
![Page 11: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/11.jpg)
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e.g. 2:
Given that the edge length of a cube ABCD.EFGH is 6 cm.The distance from point B to the diagonal of AG is…
A BCD
HE F
G
6 cm
6 cm
![Page 12: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/12.jpg)
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Solution
The distance from point B to AG = the distance from point B to P (BP AG)The side diagonal of BG = 6√2 cmThe space diagonal of AG = 6√3 cmConsider a triangle ABG !
A BCD
HE F
G
6√2
cm6 cm
P6√
3 cm
A B
G
P
6√3
6
6√2
?
![Page 13: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/13.jpg)
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Consider a triangle ABGSin A = = =
BP =
BP = 2√6
A B
G
P
6√3
6
6√2AG
BG
AB
BP
36
26
6
BP
36
)6)(26(
?
Thus, the distance from point B to AG= 2√6 cm
3
66
3
3x 2
![Page 14: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/14.jpg)
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e.g. 3
Given that T.ABCDis a pyramid. The edge length of its base is 12 cm, and the edge length of its upright is 12√2 cm. The distance from A to TC is...12 cm
12√2
cm
T
C
A B
D
![Page 15: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/15.jpg)
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SolutionThe distance from A to TC= APAC is a cube’s diagonalAC = 12√2AP = = = = Thus, the distance from 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
![Page 16: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/16.jpg)
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e.g. 4 :
Given that the edge length of a cube ABCD.EFGH is 6 cm and
A BCD
HE F
G
6 cm6 cm
Point P is in the middle of FG.
The distance from point A to line DP is…
P
![Page 17: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/17.jpg)
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A BCD
HE F
G
6 cm6 cm
P Solution
Q
6√2
cm
R
P
AD
G F
6 cm
3 cm
DP =
=
=
22 GPDG 22 3)26(
9972
![Page 18: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/18.jpg)
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Solution
Q
6√2
cm
R
P
AD
G F
6 cm
3 cmDP =
Area of ADP
½DP.AQ = ½DA.PR
9.AQ = 6.6√2
AQ = 4√2
Thus the distance from point A to line DP= 4√2 cm
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4
![Page 19: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/19.jpg)
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Perpendicular Line toward a plane
Perpendicular line toward a plane means that line is perpendicular to two intersecting lines which are located on a plane..
V
g
a
bg a, g b,
Thus g V
![Page 20: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/20.jpg)
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The Distance of a Point to a PlaneThis display shows
the distance between point A and plane V is length of line segment which connect point A to plane V perpendicularly.
A
V
![Page 21: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/21.jpg)
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e.g. 1 :
Given that the edge length of a cube ABCD.EFGHis 10 cm.Thus the distance from point A to plane is….
A BCD
HE F
G
10 cm
P
![Page 22: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/22.jpg)
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SolutionThe distance from point A to plane BDHF is representated by the length of AP (APBD)AP = ½ AC (ACBD) = ½.10√2 = 5√2
A BCD
HE F
G
10 cm
P
Thus the distance from A to plane BDHF = 5√2 cm
![Page 23: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/23.jpg)
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e.g. 2 :Given that T.ABCD is a pyramid.The length of AB = 8 cmand TA = 12 cm.The distance from point T to plane ABCD is….8 cm
T
C
A B
D
12 c
m
![Page 24: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/24.jpg)
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SolutionThe distance from T to ABCD = The distance from T to the intersection of AC and BD= TP AC is a cube’ss diagonalAC = 8√2AP = ½ AC = 4√2
8 cm
T
C
A B
D
12 c
m
P
![Page 25: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/25.jpg)
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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
Thus the distance from T to ABCD = 4√7 cm
![Page 26: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/26.jpg)
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e.g. 3 :
Given that the edge length of a cube ABCD.EFGHis 9 cm.The distance from point C to plane BDG is….
A BCD
HE F
G
9 cm
![Page 27: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/27.jpg)
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SolutionThe distance from point C to plane BDG = CPThat is the line segment which is drawn through point C and perpendicular to GT
A BCD
HE F
G
9 cm
PT
CP = ⅓CE = ⅓.9√3 = 3√3
Thus the distance from C to BDG = 3√3 cm
![Page 28: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/28.jpg)
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The Distance of line to line
This display explains the distance of line g and line h h is the length of line segment which connect those lines perpendicularly.
P
Q
g
h
![Page 29: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/29.jpg)
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e.g.Given that the edge length of a cube ABCD.EFGHis 4 cm.Determine the distance of:A B
CD
HE F
G
4 cm a.Line AB to line HG
b.Line AD to line HF
c.Line BD to line EG
![Page 30: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/30.jpg)
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SolutionThe distance of line:a.AB to line HG = AH (AH AB, AH HG) = 4√2 (a side
diagonal)b.AD to line HF = DH (DH AD, DH HF = 4 cm
A BCD
HE F
G
4 cm
![Page 31: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/31.jpg)
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Solution
The distance of:b.BD to line EG = PQ (PQ BD, PQ EG = AE = 4 cm
A BCD
HE F
G
4 cm
P
Q
![Page 32: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/32.jpg)
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The Distance of Line to Plane
This display shows the distance of line g to plane V islength of line segment which connect that line and plane perpendicularly.
V
g
g
![Page 33: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/33.jpg)
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e.g. 1
Given that the edge length os a cobe ABCD.EFGH is 8 cmThe distance of line AE to planeBDHF is….
A BCD
HE F
G
8 cm
P
![Page 34: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/34.jpg)
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SolutionThe distance of line AE to plane BDHF Is represented by the length of AP.(AP AEAP BDHF)AP = ½ AC(ACBDHF) = ½.8√2 = 4√2
A BCD
HE F
G
8 cm
P
Thus the distance from A to BDHF = 4√2 cm
![Page 35: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/35.jpg)
3535
V
W
The Distance of Plane to Plane
This display explains the distance of plane W and plane V is length of line segment which is perpendicuar to plane W and is perpendicular to plane V.
W
Jarak Dua B
idang
![Page 36: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/36.jpg)
3636
e.g. 1 :
Given that the edge length of a cubeABCD.EFGH is6 cm.The distance of plane AFH to plane BDG is….
A BCD
HE F
G
6 cm
6 cm
![Page 37: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/37.jpg)
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SolutionThe distance of plane AFHto plane BDGIs represented by PQPQ = ⅓ CE(CE is a space diagonal)PQ = ⅓. 6√3 = 2√3
A BCD
HE F
G
6 cm
6 cm
P
Q
Thus the distance of AFH to BDG = 2√3 cm
![Page 38: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/38.jpg)
3838
e.g. 2 :Given that the edge length of a cubeABCD.EFGH is 12 cm.
A BCD
HE F
G
12 cm
Points K, L and M are the middle point of BC, CDdan CG. The distance of plane AFH and KLM is….
KL
M
![Page 39: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/39.jpg)
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Solution• Diagonal EC = 12√3• The distance from E to AFH = distance from AFH to BDG = distance from BDG to CA B
CD
HE F
G
12 cm
Thus the distance from point E to AFH = ⅓EC =⅓.12√3 = 4√3So that the distance from BDG to C is 4√3 too.
L
![Page 40: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/40.jpg)
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A BCD
HE F
G
12 cm
The distance of BDG to point C is 4√3.The distance of BDG to KLM = distance of KLM to point C = ½.4√3 = 2√3
KL
M
Thus the distance of AFH to KLM = Distance of AFH to BDG + distance of BDG to KLM = 4√3 + 2√3 = 6√3 cm
![Page 41: 1 Three Dimension (Distance) After learning this slide, you’ll be able to determine the distance between the elements in the space of three dimension.](https://reader034.fdocuments.net/reader034/viewer/2022051819/551aefff5503465e7d8b4ea6/html5/thumbnails/41.jpg)
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Have a nice try !Have a nice try !