© t madas. x y 1 2 3 4 5 6 -6 -5 -4 -3 -2 1 2 3 4 5 6 -6 -5 -4 -3 -2 (3,5) consider a flat...
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![Page 1: © T Madas. x y 1 2 3 4 5 6 -6 -5 -4 -3 -2 1 2 3 4 5 6 -6 -5 -4 -3 -2 (3,5) Consider a flat horizontal surface in three dimensional space with the x and](https://reader037.vdocuments.site/reader037/viewer/2022102622/5697bf8e1a28abf838c8cc5e/html5/thumbnails/1.jpg)
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x
y
12
34
56
-6-5
-4-3
-2-1 1
23
45
6
-6-5
-4-3
-2-1
(3,5)
Consider a flat horizontal surface in three dimensional space with the x and y axes drawn. This is known as the x-y plane.Every point that lies on this plane can be uniquely identified by an ordered pair of numbers known as (cartesian ) coordinates.
![Page 3: © T Madas. x y 1 2 3 4 5 6 -6 -5 -4 -3 -2 1 2 3 4 5 6 -6 -5 -4 -3 -2 (3,5) Consider a flat horizontal surface in three dimensional space with the x and](https://reader037.vdocuments.site/reader037/viewer/2022102622/5697bf8e1a28abf838c8cc5e/html5/thumbnails/3.jpg)
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-6
-5
-4
-3
-2
-1
x
y
z
12
34
56
-6-5
-4-3
-2-1 1
23
45
6
-6-5
-4-3
-2-1 1
2
3
4
5
6
Consider a flat horizontal surface in three dimensional space with the x and y axes drawn. This is known as the x-y plane.Every point that lies on this plane can be uniquely identified by an ordered pair of numbers known as (cartesian ) coordinates.What happens for points in 3 dimensions?
(4,3,5)
xyz
![Page 4: © T Madas. x y 1 2 3 4 5 6 -6 -5 -4 -3 -2 1 2 3 4 5 6 -6 -5 -4 -3 -2 (3,5) Consider a flat horizontal surface in three dimensional space with the x and](https://reader037.vdocuments.site/reader037/viewer/2022102622/5697bf8e1a28abf838c8cc5e/html5/thumbnails/4.jpg)
© T Madas
-6
-5
-4
-3
-2
-1
x
y
z
12
34
56
-6-5
-4-3
-2-1 1
23
45
6
-6-5
-4-3
-2-1 1
2
3
4
5
6(4,3,5)
xyz
(4,3,0)
Consider a flat horizontal surface in three dimensional space with the x and y axes drawn. This is known as the x-y plane.Every point that lies on this plane can be uniquely identified by an ordered pair of numbers known as (cartesian ) coordinates.What happens for points in 3 dimensions?
![Page 5: © T Madas. x y 1 2 3 4 5 6 -6 -5 -4 -3 -2 1 2 3 4 5 6 -6 -5 -4 -3 -2 (3,5) Consider a flat horizontal surface in three dimensional space with the x and](https://reader037.vdocuments.site/reader037/viewer/2022102622/5697bf8e1a28abf838c8cc5e/html5/thumbnails/5.jpg)
© T Madas
-6
-5
-4
-3
-2
-1
x
y
z
12
34
56
-6-5
-4-3
-2-1 1
23
45
6
-6-5
-4-3
-2-1 1
2
3
4
5
6
Consider a flat horizontal surface in three dimensional space with the x and y axes drawn. This is known as the x-y plane.Every point that lies on this plane can be uniquely identified by an ordered pair of numbers known as (cartesian ) coordinates.What happens for points in 3 dimensions? (0,3,5)
![Page 6: © T Madas. x y 1 2 3 4 5 6 -6 -5 -4 -3 -2 1 2 3 4 5 6 -6 -5 -4 -3 -2 (3,5) Consider a flat horizontal surface in three dimensional space with the x and](https://reader037.vdocuments.site/reader037/viewer/2022102622/5697bf8e1a28abf838c8cc5e/html5/thumbnails/6.jpg)
© T Madas
-6
-5
-4
-3
-2
-1
x
y
z
12
34
56
-6-5
-4-3
-2-1 1
23
45
6
-6-5
-4-3
-2-1 1
2
3
4
5
6
Consider a flat horizontal surface in three dimensional space with the x and y axes drawn. This is known as the x-y plane.Every point that lies on this plane can be uniquely identified by an ordered pair of numbers known as (cartesian ) coordinates.What happens for points in 3 dimensions?
(4,0,5)
![Page 7: © T Madas. x y 1 2 3 4 5 6 -6 -5 -4 -3 -2 1 2 3 4 5 6 -6 -5 -4 -3 -2 (3,5) Consider a flat horizontal surface in three dimensional space with the x and](https://reader037.vdocuments.site/reader037/viewer/2022102622/5697bf8e1a28abf838c8cc5e/html5/thumbnails/7.jpg)
© T Madas
![Page 8: © T Madas. x y 1 2 3 4 5 6 -6 -5 -4 -3 -2 1 2 3 4 5 6 -6 -5 -4 -3 -2 (3,5) Consider a flat horizontal surface in three dimensional space with the x and](https://reader037.vdocuments.site/reader037/viewer/2022102622/5697bf8e1a28abf838c8cc5e/html5/thumbnails/8.jpg)
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x
y
z
The cuboid OABCDDEFG is located on a set of three dimensional coordinate axes, O the point with coordinates (0,0,0).The coordinates of point F are (6,4,8).Find the coordinates of points B and C.
A
BC
DE
FG
O
(6,4,8)
(6,4,0)(0,4,0)
![Page 9: © T Madas. x y 1 2 3 4 5 6 -6 -5 -4 -3 -2 1 2 3 4 5 6 -6 -5 -4 -3 -2 (3,5) Consider a flat horizontal surface in three dimensional space with the x and](https://reader037.vdocuments.site/reader037/viewer/2022102622/5697bf8e1a28abf838c8cc5e/html5/thumbnails/9.jpg)
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x
y
z
A cuboid OABCDEFG has one of its vertices at the origin as shown.The coordinates of point F are (4,3,6).1. Find the coordinates of points B, E and G.2. Find the coordinates of the midpoint of OD.
A
BC
DE
FG
O
(4,3,6)
(4,3,0)
(4,0,0)
(0,3,0)
(0,3,6)
(0,0,6)(4,0,6)
M (0,0,3)
![Page 11: © T Madas. x y 1 2 3 4 5 6 -6 -5 -4 -3 -2 1 2 3 4 5 6 -6 -5 -4 -3 -2 (3,5) Consider a flat horizontal surface in three dimensional space with the x and](https://reader037.vdocuments.site/reader037/viewer/2022102622/5697bf8e1a28abf838c8cc5e/html5/thumbnails/11.jpg)
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x
y
z
A
BC
DE
FG
O
(6,3,2)
(6,3,0)
A cuboid OABCDEFG 6 units long by 3 units wide by 2 units high is drawn on a set of 3 dimensional axes as shown below.
1. Write down the coordinates of points B and F.
2. Calculate the length of OF.
6
3
2
![Page 13: © T Madas. x y 1 2 3 4 5 6 -6 -5 -4 -3 -2 1 2 3 4 5 6 -6 -5 -4 -3 -2 (3,5) Consider a flat horizontal surface in three dimensional space with the x and](https://reader037.vdocuments.site/reader037/viewer/2022102622/5697bf8e1a28abf838c8cc5e/html5/thumbnails/13.jpg)
© T Madas
x
y
z
A
DE
G
O
A cuboid OABCDEFG 6 units long by 3 units wide by 2 units high is drawn on a set of 3 dimensional axes as shown below.
1. Write down the coordinates of points B and F.
2. Calculate the length of OF.
6
3
2
C
O A
B
3
6
OB 2 = 62+ 32
OB 2 =36+ 9
OB 2 =45
OB = 45
F (6,3,2)
B (6,3,0)
45
![Page 14: © T Madas. x y 1 2 3 4 5 6 -6 -5 -4 -3 -2 1 2 3 4 5 6 -6 -5 -4 -3 -2 (3,5) Consider a flat horizontal surface in three dimensional space with the x and](https://reader037.vdocuments.site/reader037/viewer/2022102622/5697bf8e1a28abf838c8cc5e/html5/thumbnails/14.jpg)
© T Madas
x
y
z
A
DE
G
O
A cuboid OABCDEFG 6 units long by 3 units wide by 2 units high is drawn on a set of 3 dimensional axes as shown below.
1. Write down the coordinates of points B and F.
2. Calculate the length of OF.
6
3
2
C
O B
F
2
F (6,3,2)
B (6,3,0)
45
45
OF 2 =22+ 45 2
OF 2 = 4 + 45
OF 2 =49
OF = 7
![Page 15: © T Madas. x y 1 2 3 4 5 6 -6 -5 -4 -3 -2 1 2 3 4 5 6 -6 -5 -4 -3 -2 (3,5) Consider a flat horizontal surface in three dimensional space with the x and](https://reader037.vdocuments.site/reader037/viewer/2022102622/5697bf8e1a28abf838c8cc5e/html5/thumbnails/15.jpg)
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