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8.7.5 Vectors, SPM Practice (Question 9)


Question 9:
Diagram 2 shows a triangle EFG.



It is given ER:RF=1:2, FG:TG=3:1, ER=4x˜ and EG=6y˜.It is given ER:RF=1:2, FG:TG=3:1, ER=4x˜ and EG=6y˜.
a) Express in terms of x˜ and y˜: (i) GR (ii) GT
[3 marks]
(b) If line GR is extended to point K such that GK=hGR and EK=6x˜3y˜, find the value of h.
[3 marks]


Solution:
(a)(i)
GR=GE+ER=6y˜+4x˜

(a)(ii)
GT=13GF=13(GR+RF)=13(6y˜+4x˜+8x˜)RF=2ER=2y˜+4x˜

(b)
GK=hGRGE+EK=hGR6y˜+(6x˜3y˜)=h(6y˜+4x˜)9y˜+6x˜=6hy˜+4hx˜Compare,6h=9h=32


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