3 easy question

1)Let H be a point on CE such that FH // AD ,
then
CG : GH = CD : FH
CG : GH = CD : BC
CG : GH = 1 : 2and
HE : CH = EF : FA = BC : AB = 1 : 1
i.e. HE = CH = CG + GH

So
CG : GE
= CG : (GH + HE)
= CG : (GH + CG + GH)
= 1 : (2 + 1 + 2)
= 1 : 5Choose (D).

2)The x - coordinates of A , B are the roots of x² + (0)² - 2x - 7(0) - 8 = 0
x² - 2x - 15 = 0
(x - 5)(x + 3) = 0
x = 5 or x = - 3 are the x - coordinates of A , BThe length of AB = 5 - (-3) = 8.

3)Let (x , y) be C.AB : BC = (14 - 2) : (2 - y)
2 : 1 = 12 : (2 - y)
y = - 4AB : BC = (7 - 1) : (1 - x)
2 : 1 = 6 : (1 - x)
x = - 2The coordinates of C is (- 2 , - 4).

2012-07-27 23:02:52 補充：
Method 2 for Q1 :

CG = BF * CD/BD = BF * 1/(2+1) = BF/3

CE = 2BF

So CG : GE = CG : (CE - CG) = BF/3 : (2BF - BF/3) = 1/3 : (2 - 1/3) = 1 : 5
Ans : (D)

2012-07-27 23:10:34 補充：
Correction of Q2 :

The x - coordinates of A , B are the roots of

x² + (0)² - 2x - 7(0) - 8 = 0
x² - 2x - 8 = 0
(x - 4)(x + 2) = 0
x = 4 or x = - 2 are the x - coordinates of A , B

The length of AB = 4 - (-2) = 6.

2012-07-27 23:23:09 補充：
Correction of Q2 :

The x - coordinates of A , B are the roots of

x² + (0)² - 2x - 7(0) - 8 = 0
x² - 2x - 8 = 0
(x - 4)(x + 2) = 0
x = 4 or x = - 2 are the x - coordinates of A , B

The length of AB = 4 - (-2) = 6.