© T Madas

© T Madas

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.

© 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?

(4,3,5)

xyz

© 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?

© 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)

© 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)

© T Madas

© T Madas

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)

© T Madas

© T Madas

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)

© T Madas

© T Madas

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

© 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

© 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

© T Madas