Fei Fei Math Q7

[JS]

7.一直線 L 過點 A(5,0), B(0,2)坐標原點為 O, 點 P(X,Y) 為三角形OAB的一點,
求Y<X的機率

at the fei fei's explaination, I dont understand the part how he figure out the line x=y interecpt with line AB at (10/7, 10/7).
Can someone help me out here,pls?

Thx!!!

[Calvin]

using equation "y=ax+b", u can get the equation of line L.

then u can get the intercept of L and x=y.

[JS]

using equation "y=ax+b", u can get the equation of line L.

then u can get the intercept of L and x=y.

thx calvin.

just in case someone has the same question as I do. the following is the detailed explaintion I get from yahoo.

過ＡＢ的直線方程式是　Ｌ：２ｘ＋５ｙ＝１０　
假設令一條直線　Ｌ１：ｙ＝ｘ　即　ｘ－ｙ＝０
(this is the part I did not understand b4. Because I didnt know that by using two line equations and solving x, y, one can get the intercept point of the two.)
兩條直線的交點是　Ｃ（１０/７，１０/７）

在直線Ｌ１的右半邊都是ｙ＜ｘ　反之　在直線Ｌ１的左半邊都是ｘ＜ｙ

如果想要知道ｙ＜ｘ的機率
那就求直線Ｌ１的右半邊與三角形ＯＡＢ相交的面積Ａ２
在除以三角形ＯＡＢ的面積Ａ１即可

三角形ＯＡＢ的面積是　Ａ１＝(１/２)*２*５＝５
Ａ２＝(１/２)*(１０/７)*５＝２５/７

那ｙ＜ｘ的機率是　(２５/７)/５＝５/７