Apps. and Interpretation for IBDP Maths Ebook 1 | Page 103

Exercise 28
1. In a three-dimensional coordinate system with vertical z -axis, the coordinates of the
point A are ( �14, � 48, 0) . O is the origin.
(a) Find the coordinates of M , the mid-point of OA .
The point N is vertically above the point M by n units, where n � 0 . It is given that
ON � 65 .
[2]
(b) (i) Write down the coordinates of N , giving the answer in terms of n .
(ii) Find the value of n .
[3]
2. In a three-dimensional coordinate system with vertical z -axis, the coordinates of the
point P and Q are (15, 25, 35) and (45, 85,15) respectively.
(a) Find the length of PQ .
(b) Find the coordinates of M , the mid-point of PQ .
The point N is vertically below the point M by 20 units.
[2]
[2]
(c) (i) Write down the coordinates of N .
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(ii) Hence, find the length of QN .
[3]
3. In a three-dimensional coordinate system with vertical z -axis, the coordinates of the
point A and B are (12, �2, � 8) and ( � 24, 30, 4) respectively.
(a) Find the coordinates of M , the mid-point of AB .
[2]
M is translated 40 units in the positive x direction, following by another translation of 9
units in the positive y direction to reach the point N .
(b) Find the length of MN .
N is translated upward by 30.75 units to reach the point P .
(c) Find the angle of elevation of P from M .
[2]
[2]
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