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 =4 x ˜  and  EG =6 y ˜ .
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 =h GR  and  EK =6 x ˜ 3 y ˜ , find the value of h.
[3 marks]


Solution:
(a)(i)
GR = GE + ER =6 y ˜ +4 x ˜

(a)(ii)
GT = 1 3 GF = 1 3 ( GR + RF ) = 1 3 ( 6 y ˜ +4 x ˜ +8 x ˜ ) RF =2 ER =2 y ˜ +4 x ˜

(b)
GK =h GR GE + EK =h GR 6 y ˜ +( 6 x ˜ 3 y ˜ )=h( 6 y ˜ +4 x ˜ ) 9 y ˜ +6 x ˜ =6h y ˜ +4h x ˜ Compare, 6h=9 h= 3 2


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