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2. 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. y 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1
(3,5) x
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3. What happens for points in 3 dimensions? z x y z
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? z x y z 6 ( 4 ,3 ,5 ) 5 4 y 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 3 2 1 -1 -2 -3 x -4 -5 -6
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4. What happens for points in 3 dimensions? z x y z
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? z x y z 6 ( 4 ,3 ,5 ) 5 4 y 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 3 2 1 ( 4 ,3 ,0 ) -1 -2 -3 x -4 -5 -6
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5. What happens for points in 3 dimensions? z
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? z ( ,3 ,5 ) 6 5 4 y 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 3 2 1 -1 -2 -3 x -4 -5 -6
© T Madas

6. What happens for points in 3 dimensions? z
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? z 6 5 ( 4 ,0 ,5 ) 4 y 1 2 3 4 5 6 -6 -5 -4 -3 -2 -1 3 2 1 -1 -2 -3 x -4 -5 -6
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8. 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. z G F ( 6 ,4 ,8 ) E D y C B ( 6 ,4 ,0 ) ( ,4 ,0 ) O x A
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10. 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. G F z ( ,3 ,6 ) ( 4 ,3 ,6 ) E ( 4 ,0 ,6 ) D ( ,0 ,6 ) y M ( ,0 ,3 ) C B ( 4 ,3 ,0 ) ( ,3 ,0 ) O x A ( 4 ,0 ,0 )
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12. 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. z y G F ( 6 ,3 ,2 ) D 2 E C B ( 6 ,3 ,0 ) 3 O x 6 A
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13. 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. B z 3 y G F ( 6 ,3 ,2 ) O A 6
OB 2 = 62
+ 32 c D 2 E
OB 2 = 36
+ 9 c C B
OB 2 = 45 c ( 6 ,3 ,0 )
OB = 45 3 45 O x 6 A
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14. 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. z F 2 y G F ( 6 ,3 ,2 ) O B 45 D 2
OF 2 = 22 c E
OF 2 = 4
+ 45 c C B ( 6 ,3 ,0 )
OF 2 = 49 c 3
OF = 7 45 O x 6 A
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