F.4 MATHS

As follows:

圖片參考：http://i707.photobucket.com/albums/ww74/stevieg90/11-20.jpg

13(a).　其實要找equation, 先要找到slope& one point,

　　　你e+ form4,應該知道general form, 即是Ax+By+C=0
由於AD//BC,所以 slope of AD&BC are the same.
Ax+By+C=0
By= -Ax-C
y= -A/B-C/B
所以-A/B就是slope, -C/B is y-intercept
2x+y-4=0
slope of AD= -2/1= -2
slope of BC= -2
已知C(8,2)
Equation: (y-2)/(x-8)= -2
y-2= -2(x-8)
y-2= -2x+16
y= -2x+18
2x+y-18=0

13(bi). equation: slope + one point
要先知 the coordinates of A
Let the coordinates of A be (0,y),
Put (0,y) into the equation of AD 2x+y-4=0,
2(0)+y-4=0
0+y-4=0
y=4
所以A(0,4) (已有one point)
跟住要搵 the coordinates of D
Put (x,0) into the equation of AD 2x+y-4=0
2x+0-4=0
2x-4=0
2x=4
x=2
D(2,0) (點解要知道D呢..因為equation要有one point+slope,而e+只欠slope,如果要找slope,就要知道DC個equation)
e+有２個point D(2,0) , C(8,2) ,其實有２個point 都可以找到equation
(y-2)/(x-8)=(2-0)/(8-2)
=1/3
(y-2)*3=(x-8)*1
3y-6=x-8
3y-x+2=0
slope of DC: -A/B= -(-1)/3
=1/3
slope of AB=1/3 (又有slope & one point)
Equation: (y-4)/(x-0)=1/3
(y-4)*3= x*1
3y-12=x
3y-x-12=0

13(bii). 由於已知　the equation of AB&BC,所以就會知道 the coordinates of B (分２條式）
　　　 3y-x-12=0----1
2x+y-18=0----2

1*2, 6y-2x-24=0---3
2+3, 7y-42=0
7y=42
y=6
Put y=6 into 1,
3(6)-x-12=0
18-x-12=0
x= -6
B(-6,6)
Hope that can help you^^

2010-07-17 18:48:11 補充：
最後有小小更正，
x=6, 不是-6
因為　　１８－ｘ－１２＝０
　　　　－ｘ＋６＝０
　　　　ｘ＝６
　　　所以B（６，６）
ｓｏｒｒｙ．．