问题 填空题

在平面直角坐标系中,A(2,0),B(3,0),P是直线y=x上的点,当PA+PB最小时,P点的坐标为______.

答案

如图,作A关于直线y=x的对称点A′,

则PA=PA′,

故PA+PB=PA′+PB,

由图知,只有当A、P、B共线时,PA+PB最小,

又由A与A′关于y=x对称知,A′(0,2),

由A′、B两点坐标得A′B直线方程:

x
3
+
y
2
=1,

联立

x
3
+
y
2
=1
y=x

解得 x=y=

6
5

故当PA+PB最小时,P的坐标为:(

6
5
6
5
).

故答案为:(

6
5
6
5
).

阅读理解

阅读理解。

                                                             Studying too much?

     Kids enjoying their weekend in Fujian by picking fruit NEWSPHOTOMost people work or study from Monday to Friday. The weekend is usually a time of rest. But today's Chinese teenagers can hardly rest during the weekends.

According to a survey, 24% of the Grade 8 students in Beijing have classes at the weekend. Over 40% of the middle school students have less than eight hours sleep each night because of study.

And this isn't only in Beijing. Ji Chunying is a Grade 9 student in Guangzhou. The 14-year-old has to get up at 6:45 am on Saturday. Then she has a whole day of classes. On Sunday, she goes to extra* classes for math and physics.

     But Ji doesn't complain. She says her classmates all work very hard.

                                                        Finding time to have fun

     Zhao Yang, 13, is from Dalian, Liaoning. As a Grade 8 student, Zhao's weekend is less busy. But he still spends Saturday in school. On Sunday, after finishing homework, he plays basketball. "I feel happy because I still have time to do the things I like," he said.

     Some students are much luckier. They don't have to go to school on the weekend.

     Ding Yi, a Grade 8 student from Laiwu, Shandong, is one of them. And she's a top student.

     During the weekend, Ding usually gets up at 8 am. Then she spends some time doing homework. After that she is free to go shopping or watch TV.

     Ding said her mother once wanted her to try extra classes. But when they asked Ding's teacher about it, the teacher said it was unnecessary.

     "My teacher said I don't need to push myself too much. Learning well at school is enough," Ding said. "I feel pretty lucky."

1. Over 40% of the middle school students have less than eight hours sleep each night because of ______.

A. playing computer games

B. playing with friends

C. busy study

D. watching TV

2. How many students are mentioned in this passage?

A. 2.

B. 3.

C. 4.

D. 5.

3. We can learn from the passage that _______.

A. Some middle school students can enjoy their weekend.

B. All the students in China are busy studying on the weekend.

C. Every student in China has to go to extra classes on the weekend.

D. All the students complain about their busy weekend.

4. The above text may be a _______.

A. a story of science

B. school notice

C. short play

D. news report

选择题