f3 Maths問題X3..好急架!!!15分呀!!

1.A(3,4), B(x,5) and C(1,3) are three points with A,B,C on a same straight line.
Find x.
Equation of AC: y-3=[(4-3)/(3-1)](x-1)
y=(1/2)(x-1)+3
2y=x-1+6
2y=x+5
Since B lies on AC, 2(5)=x+5
10=x+5
x=5
2.The perpendicular bisectors of the sides AB, AC of any triangle ABC intersect at point O. Prove that OB=OC.(冇圖)
In triangle ABC, Let the bisectors be point D and E,
such that OD perpendicular to AB and bisects AB;
OE perpendicular to AC and bisects AC.
EB=CE
By Pyth. theorem,
OB^2=OE^2+EB^2
OC^2=OE^2+CE^2
=OE^2+EB^2
=OB^2
Hence, OC=OB
3.雖然睇唔清楚,,,希望無睇錯la~
Since rhombus is a kind of //gram,
DK=KB(properties of //gram)
5x-1=8x
-1=3x
x=-1/3

2010-01-20 20:39:40 補充：
改正:#3
KC=(5x-1)
KB=8x
Since rhombus is a kind of //.gram
AK=KC=5x-1(properties of //.gram)









2010-01-20 20:42:07 補充：
By Pyth. theorem,
10^2=AK^2+KB^2
100=(5x-1)^2+64x^2

2010-01-20 20:42:49 補充：
89x^2-10x-99=0
(89x-99)(x+1)=0
x=99/89 or -1(rej.)

2010-01-20 20:50:34 補充：
首先我解釋等1題先,,,
Equation of AC: y-3=[(4-3)/(3-1)](x-1)<===點黎?
首先,,, Slope of AC = [(4-3)/(3-1)]
(y-y_1)/(x-x_1)=Slope of AC.
y-y_1=Slope of AC *(x-x_1)
所以有AC既equation,
跟住因為B於AC的equation線上,,,因此B的坐標一定適合於AC的equation

2010-01-20 20:55:44 補充：
跟住等2題,,,你問D同E8點黎
因為題目話The perpendicular bisectors of the sides AB, AC of any triangle ABC intersect at point O. ,,,因此我設由O延伸至遇到AB於D點,和O延伸至遇到AC於E點,,,以及OD垂直於AB,,,OE垂直於AC

2010-01-20 20:57:03 補充：
89x^2-10x-99=0
(89x-99)(x+1)=0<-用交叉相乘
x=99/89 or -1(rej.) 因為8x>0,x>0
所以x不可能是-1

2010-01-20 20:58:38 補充：
"to deathnotesimonxdd:
um..其實呢..
我覺得係ck=5x-1
唔係dk=5x-1- -"
如果係我咁解會唔會計唔到??"響補充到做番~

2010-01-20 21:33:12 補充：
first,基本上都睇得明
不過你一開始第2題個答案寫eb=ce
其實係咪應該係eb=cd??唔係,,,因為我寫左E bisects BC into 2 equal parts
所以EB=EC而唔係CD

2010-01-20 21:35:34 補充：
second,第1題係咪一定要用2個未知數?這只是Gerneral formula,,,你可以用其他方法
用1個o唔ok(其實我可唔可以用1個未知數去express另一個未知數,例如express a
in terms of b咁?姐係如果a=1,b=2,咁b=0.5a),,ok你可以let f(x)=mx+C等等,,,
C is the y-intercept.
我只是提供其中一個解決方案

2010-01-20 21:38:15 補充：
third,(89x-99)(x+1)=0呢度其實係咪cross method..係
交叉相乘唔係分數果陣先用架咩-.-例如:1/2x=5/8,,8=10x<===lee個好係唔係cross method- -[如果無記錯的話]只係個product屬於cross product姐
cross method 多用於把 quadratic equation化為因子
例如： 89x^2-10x-99 變成 (89x-99)(x+1)

2010-01-20 21:40:34 補充：
有唔識係正常既~~如果識你都唔好問啦~~~其實，最重要係你明姐,,,如果唔明，我都會盡諒解釋到你明
加上我拎既係你既分，是一種交易，而令你明白也是我的責任
[當然我也樂於這樣做，同時可以practice嘛^^"]

2010-01-22 20:19:40 補充：
1.A(3,4), B(x,5) and C(1,3) are three points with A,B,C on a same straight line.
Find x.
(4-3)/(3-1)=(5-3)/(x-1)
1/2=2/(x-1)
x-1=4
x=5
咁講啦~因為A,B,C同時響同一條直線上，證明A,B,C同樣適用於同一條方程式,而同一條方程式有一樣的斜率，所以AC同AB同BC有同一斜率

2010-01-22 20:21:38 補充：
第2題當然可以用congruent triangle去solve,,,一題數係可以有多種唔同方法去solve...
[p.s.特別是trigonometry方面的question]

中三好像據我所知, 仲未學到form equation of line.
第一條係points collinear 問題
三個pts 都係同一線上
三個pts 都係collinear.
Hence,
Slope of AB = Slope of BC.
And solve x.