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] 92 SE Production Limited