问题 解答题

直线l过点(2,4)被两平行直线x-y+1=0,x-y+2=0所截得的线段的中点在直线x+2y-3=0上,求此直线l的方程.

答案

记直线l与两平行线的交点为A、B,AB的中点为C,

则由题意知点B在直线x-y+2=0上,即B(2,4).             …(2分)

设A(x0,y0),

则AB的中点C的坐标为(

x0+2
2
y0+4
2
).          …(4分)

因为点C在直线x+2y-3=0上,

所以

x0+2
2
+2×
y0+4
2
-3=0,

即x0+2y0+4=0.                                           …(6分)

又x0-y0+1=0,

所以由

x0+2y0+4=0
x0-y0+1=0.

得A(-2,-1).       …(9分)

故直线l的方程为:5x-4y+6=0.                             …(12分)

阅读理解

Students Begin to Smoke at a Younger Age

SHANGHAI---- Almost one in four students aged between 12 and 14 have tried smoking, according to the results of a survey from the CATC(中国抗癌协会).

“ Quite a number of boy students in my class smoke outside the school yard during lunch break,” said Li Xiaolan, an English teacher from a high school in Shanghai.

The survey also found that 39 percent of students took their first cigarette from their classmates.

“ It was quite common to smoke with my classmates at school,”said Zhou Guangrong,a 22- year–old university student from Guiyang, Guizhou province,who started smoking at the age of 12.

Most of the student smokers buy cigarettes themselves.” My middle and high schools were surrounded by cigarette shops when I was a student,” said Liu Minghui who used to smoke two cigarettes per day in primary school and two packs per week in middle and high school.

“ We’re keen to show that more teenagers are starting smoking much younger than before,and that we need to minimize(降低) the number of young smokers,” said Duan Jiali, an officer in CATC. He added that teachers and parents should set a good example for teenagers by not smoking in front of them at school or at home, which is the best way of stopping teenagers from smoking.

小题1:According to the survey,in a middle school if a class has 40 students, about _____ smoke.

A.5

B.10

C.15

D.20小题2:Many boy students smoke ________during lunch break.

A.at home

B.in class

C.in the office

D.outside the school yard小题3:The survey found that 39 percent of students took their first cigarette from ________.

A.their parents

B.their teachers

C.their brothers

D.their classmates小题4:From the passage we know ________smokes two packs per week in middle and high school.

A.LI Xiaolan

B.Zhou Guangrong

C.Liu Minghui

D.Duan Jiali小题5:Which of the following is NOT true according to the passage?

A.More teenagers are starting smoking much older than before.

B.Most of student smokers buy cigarettes themselves.

C.Some students smoke in toilets or in corners of the playground after lunch.

D.Teachers and parents shouldn’t smoke.

多项选择题