3D Coordinates

• OA = 8 units.
• OC = 5 units.
• OG = 6 units.
• M is the midpoint of DE.
• N is the point at the centre of the base.

(a)  Write down the coordinates of A.

• OA = 8 units.
• OC = 5 units.
• OG = 6 units.
• M is the midpoint of DE.
• N is the point at the centre of the base.

(b)  Write down the coordinates of D.

• OA = 8 units.
• OC = 5 units.
• OG = 6 units.
• M is the midpoint of DE.
• N is the point at the centre of the base.

(c)  Write down the coordinates of E.

• OA = 8 units.
• OC = 5 units.
• OG = 6 units.
• M is the midpoint of DE.
• N is the point at the centre of the base.

(d)  Write down the coordinates of M.

• OA = 8 units.
• OC = 5 units.
• OG = 6 units.
• M is the midpoint of DE.
• N is the point at the centre of the base.

(e)  Write down the coordinates of N.

The apex D is directly above the centre of the base.

The height of the pyramid equals the length of its base.

Write down the coordinates of D.

The diagram shows a cube placed on top of a cuboid, relative to the coordinate axes.

A is the point (8,4,6).
Write down the coordinates of B and C.

The diagram shows a square-based pyramid placed on top of a cube, relative to the coordinate axes.

The height of the pyramid is half of the height of the cube.
A is the point $\displaystyle (6,0,0).$
The point C is directly above the centre of the base.
Write down the coordinates of B and C.

The diagram shows a triangular prism, ABCDEF, relative to the coordinate axes.

$\displaystyle A(4,0,5)$, $\displaystyle E(2,0,0)$.
$\displaystyle AD=AE$, $\displaystyle DC=8$ units.
Edges EF, DC and AB are parallel to the y-axis.
Write down the coordinates of B and C.

The diagram shows a cone with diameter 6 units and height 8 units.

•  The x-axis and the y-axis are tangents to the base
•  A is the point of contact between the base and the x-axis
•  B is directly above the centre of the base
Write down the coordinates of A and B.

The diagram shows a hemisphere relative to the coordinate axes.

•  A is the point (6,0,0)
•  C is the midpoint of diameter OA
•  B is vertically below C
State the coordinates of B.

The diagram shows a cuboid, KLMNOPQR, relative to the coordinate axes.

L has coordinates (0, 3, 12).
R has coordinates (4, 0, 0).
(a)  Write down the coordinates of M.
(b)  Calculate the length of the space diagonal OM.