Apps. and Interpretation for IBDP Maths Ebook 1 | Page 102

Your Practice Set – Applications and Interpretation for IBDP Mathematics
28
Paper 1 – Three-Dimensional Space
Example
In a three-dimensional space, the coordinates of the point P are (4, 6,12) .
(a)
Find the length of OP , where O is the origin.
(b) Find the coordinates of M , the mid-point of OP .
The coordinates of the point A are ( x ,15, 6) . It is given that MA � 13 .
[2]
[2]
(c) Find the possible values of x .
[3]
Solution
(a)
(b)
(c)
The length of OP
2 2 2
� (4 �0) � (6 � 0) � (12 � 0)
(A1) for substitution
� 14
A1 N2
The coordinates of M
�0 � 4 0 � 6 0 �12
�
� � , , �
(A1) for substitution
� 2 2 2 �
� (2, 3, 6)
A1 N2
2 2 2
( x � 2) � (15 �3) � (6� 6) � 13
(M1) for setting equation
2
( x � 2) �144 � 13
2
( x � 2) �144 �13 � 0
By considering the graph of
y
2
� ( x� 2) �144 � 13 , 3
x �� or x � 7 . A2 N3
[2]
[2]
[3]
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