A cuboid with sides of length 5, 4 and 3 is shown in the diagram.
The origin is at the point O and the coordinates of the point A are (5,4, 3).
1 Write down the coordinates of B, C and D.
If A and B are two points [AB] should be read as "the line
segment with A and B as end points".
2 Write down the coordinates of the midpoint of [OA] and [BC].
3 Hence conjecture a formula for finding the mid-point of the line segment joining (X, Y,, 2,) and (X2, Y, 7,).
4 a Use your formula to find the midpoint of [BD].
b How can you use a previous answer to verify the formula works?
If A and B are two points AB should be read as "the length of the line segment with A and B as end points" or "the length of [AB]".
5 a Use Pythagoras' theorem to find BC. b Hence find BD.