有冇人知道中點定理係咩????請快d回答!!!!

即係midpoint theorem, 如下:

一個三角形ABC的兩條邊AB and CA 既midpoint F and G

length of FG = 1/2 length of BC
FG//BC
AFG is similar to ABC

圖片參考：http://hk.geocities.com/abcsghk/mid-pt_thm.gif

圖中，AD = DB 及 AE = EC
則D為AB的中點，E為AC的中點。
當D (x,y)是線般AB的中點時，也就是AD = DB ，則AD/DB = 1
即m:n = 1:1。截點公式可化簡為：
x = x1+ x2 / 2 ，y = y1+ y2 / 2
以上公式為中點公式。

例子:A的坐標是(-5，8)和B的坐標是(-9，-12)，AB連成一直線
(a)若P點是AB的中點，求P點的坐標。
設P點的坐標是(x，y)
x = (-5)+(-9) / 2
x = -14/2
x = -7

y = 8+(-12) / 2
y = -4/2
y = -2
∴P點的坐標是(-7 , -2)
A及B的坐標為(3, -1)及(8,4)，Q為AB的中點，求Q點的坐標。
設Q點的坐標是(x，y)
x = 3+8 / 2
x = 11 /2
x = 5.5

y = -1+4 / 2
y = 3 /2
y = 1.5
∴Q點的坐標是(5.5 , 1.5)

截點公式
若P點把A(x1，y1)和B(x2，y2)以m:n的比分成兩部分
則P點的坐標是
x = (nx1+mx2)/m+n
y = (ny1+my2)/m+n


(b)若P點把AB以2:3的比分成兩部分，求P點的坐標。
設P點的坐標是(x，y)
x = (-5)3+(-9)2/2+ 3
x = (-15)+(-18)/5
x = -33/5
x = -6.6

y = (8)3+(-12)2/2+3
y = 24+(-24)/5
y = 0
∴P點坐標是(-6.6，0)

http://www.jimloy.com/cindy/midpoint.htm

http://mathworld.wolfram.com/ArchimedesMidpointTheorem.html

http://mathworld.wolfram.com/Midpoint.html

http://www.gomath.com/messageboard/index.php?message=48718

There are two version of Mid-Point Theorem. The first two links above belongs to Version I while the remaining links belongs to Version II. I don't know whick version did u need. Hope this will still help you.