5 A(2,3),B(¡ 1 ,5),C(¡ 1 ,1) and D(¡ 7 ,5) are four points in the Cartesian plane.a Find¡!
AB and¡!
CD:
b Explain why¡!
CD is parallel to¡!
AB:
c E is the point(k,1)and¡!
AC is parallel to¡!
BE. Findk.6 In triangle ABC, M and N are the midpoints of AB and AC
respectively.
a Is MN parallel to BC?
b Prove your answer toausing vector methods.7 Consider the points A(2,3),B(4,7) and C(¡ 2 ,¡5):a Find¡!
AB and¡!
BC. b Is there a numberksuch that¡!
BC=k¡!
AB?
c
8 Consider the quadrilateral ABCD for which P, Q, R and S are
the midpoints of its sides.
a Find the coordinates of P, Q, R and S.
b Find¡!
PQ and¡!
SR:
c Find¡!
SP and¡!
RQ.
d What can be deduced about quadrilateral PQRS?Vectors can be used to establish relationships between the line segments in geometric shapes. We can use
these relationships to prove geometrical facts.Example 16 Self Tutor
Find, in terms of r,sandt:a¡!
RS b¡!
SR c¡!
ST
a¡!
RS
=
¡!
RO+
¡!
OS
=¡
¡!
OR+
¡!
OS
=¡r+s
=s¡rb¡!
SR
=
¡!
SO+
¡!
OR
=¡
¡!
OS+
¡!
OR
=¡s+r
=r¡sc¡!
ST
=
¡!
SO+
¡!
OT
=¡
¡!
OS+
¡!
OT
=¡s+t
=t¡sH VECTORS IN GEOMETRY [5.2]
MA,()2 ¡1 NB,()4 ¡7C,()10 ¡3PQRSA,()-4 ¡2
D,()4 ¡6B,()-2 ¡8 C,()6 ¡8r stR SO TVectors (Chapter 24) 499Explain what your result inbmeans.IGCSE01
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Y:\HAESE\IGCSE01\IG01_24\499IGCSE01_24.CDR Monday, 10 November 2008 10:02:53 AM PETER