Apps. and Interpretation for IBDP Maths Ebook 1 | Page 120

Your Practice Set – Applications and Interpretation for IBDP Mathematics
33
Paper 1 – Equations of Perpendicular Bisectors
Example
Consider the points A(4, 2) and B(8, 8) .
(a) Find the coordinates of C , the mid-point of AB .
(b) (i) Find the gradient of AB .
[2]
(c)
(ii) Hence, write down the gradient of the straight line perpendicular to AB .
[3]
Find the equation of the perpendicular bisector of AB , giving the answer in
slope-intercept form.
[2]
Solution
(a)
The coordinates of C
�4 �8 2 �8
�
� � , �
(A1) for substitution
� 2 2 �
� (6, 5)
A1 N2
(b) (i) The gradient of AB
8�
2
� (M1) for valid approach
8 � 4
3
� A1 N2
2
(ii)
2
� A1 N1
3
(c) The equation of the perpendicular bisector of AB :
2
y�5 � � ( x� 6)
3
(M1) for substitution
2
y�5� � x�
4
3
2
y� � x� 9
3
A1 N2
[2]
[3]
[2]
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