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=h→GR and →EK=6x˜−3y˜, find the value of h.
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=6x˜−3y˜, find the value of h.
[3 marks]
Solution:
(a)(i)
→GR=→GE+→ER=−6y˜+4x˜
(a)(ii)
→GT=13→GF=13(→GR+→RF)=13(−6y˜+4x˜+8x˜)←→RF=2→ER=−2y˜+4x˜
(b)
→GK=h→GR→GE+→EK=h→GR−6y˜+(6x˜−3y˜)=h(−6y˜+4x˜)−9y˜+6x˜=−6hy˜+4hx˜Compare,−6h=−9h=32