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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 © T Madas
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 © T Madas
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 © T Madas
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
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 © T Madas
© T Madas
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 © T Madas
© T Madas
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 ) © T Madas
© T Madas
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 © T Madas
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 © T Madas
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 + 45 2 c E OF 2 = 4 + 45 c C B ( 6 ,3 ,0 ) OF 2 = 49 c 3 OF = 7 45 O x 6 A © T Madas
© T Madas