已知△ABC的三个顶点A(1,2)、B(4,1)、C(3,4)在AB边上求一点P,使得过点P作平行于BC的直线PQ把△ABC的面积分

已知△ABC的三个顶点A(1,2)、B(4,1)、C(3,4)在AB边上求一点P,使得过点P作平行于BC的直线PQ把△ABC的面积分

P(1+3根号2/2,2+3根号2/2)。
y=-3x+5+4根号2.追问详细过程追答先写出表达式AB:y=-1/3 (x-1)+2=-1/3x+7/3
BC:y=-3(x-3)+4=-3x+13
AC:y=x+1
∵P在AB上 可设P(a,-1/3a+7/3)
∵PQ//BC
∴PQ: y=-3(x-a)-1/3a+7/3=-3x+8/3a+7/3
又 AC表达式 联立得Q（2a/3+1/3,2a/3+4/3 ）
∵PQ//BC
∴三角形AQP∽ACB 又面积相等
AQ^2：AC^2=1:2 则
[（2a/3+1/3-1)^2+(2a/3+4/3-2)^2 ]:(2^2+2^2)=1:2
解得：a=1+3根号2/2 a=1-3根号2/2(舍去）( ∵a>1)
∴PQ： y=-3x+8/3+4根号2+7/3 =-3x+5+4倍的根号2.

you remember Guangzhou Xu Ting it? The more young people to use ATMs error fled after the teller 175,000 yuan, the court was sentenced to life imprisonment for theft, commuted to imprisonment for 5 years.
now, Shenzhen appear comparable with the controversial case of Xu Ting: thousand dollars of monthly income in Shenzhen airport cleaning woman Liang, in the trash next to the gold jewelry. Liang judiciary may be prosecuted for theft, if convicted, because a huge amount, Liang faces a maximum penalty of life imprisonment.
Guangzhou Daily reported that a 5 months after the incident, the case also added the investigation stage, the prosecution has not yet determined what charges to prosecute for Liang.
Liang case in the legal profession has caused great concern in Shenzhen, Shenzhen University School of Law professors believe that this is a classic case, Liang can be called in Shenzhen, worse than a majority Xu Ting, a strong social universality, you can write textbooks, law school professor has even put the case onto the classroom to the students to discuss.
picked up in the trash can next to the small carton

not open to see first on the toilet

case protagonist Liang, 40 years old, Kaifeng, Henan people, XingJu is a cleaning company before the employees responsible for Shenzhen Airport departure hall of Terminal B building clean. By the Shenzhen Public Security Bureau issued a prosecution submissions described the incident process:

the morning of December 9 last year,escarpins louboutin, Liang as usual at the airport waiting hall cleaning. When she first went to 19 check-in counter, I saw two female passengers near the trash in Kegua Zi, among them there is a baggage car, the car stood a small cardboard box. After a 56 minutes, two passengers hurriedly ran into the security gate.
Liang second trash can next to the counter 19 to see the little cardboard box is still baggage car,louboutin pas cher, they thought it was abandoned, left to see no one, they pulled the little paper discard box as clean to clean the car. Liang then continue working in the hall.
about 9 o'clock, Liang told his colleague Jo called Since then, Liang and other cleaners with breakfast, and tell you it picked up a small cardboard box.
worker named Ma and Jo went to the bathroom open the carton, and discovered a bag of gold jewelry. They split out two packets of jewelry and left. Work fast when Jo told Liang, cartons may be built of gold jewelry.
Liang does not believe, come up with a piece of jewelry from the carton, so that colleagues Korean English to get the hall of gold jewelery inquiry. Han Liang told the British came back, this jewelry and jewelers in the selling of gold jewelry is the same. Liang Han Ying and kidding themselves that, after work at noon to put a small cardboard box back to their own home.
owner said a temporary leave 10 minutes

back boxes disappeared

evening around 6 pm, two police officers came to the Liang family. Liang took out the cardboard box from under the bed to them. The police took a man to the police station Liang.
the original, the same day at about 9 am, the airport police station received a tempest Tengye man reported, he said he was Houjie Town Dragon jewelry company employees, at 8 o'clock in the counter 19 baggage handling procedures, the airport staff told him that valuables can not be checked, he was so counter 22 to 19 meters away from the counter 10 to find consulting director on duty,Christian Louboutin pas cher, yet equipped with 14 kilograms of gold jewelry in a small cardboard box on the luggage car, parked on the baggage car No. 19 at the counter next to the trash. 10 minutes later, when Wang Teng industry back to its home and found cartons missing, police hastily.
evening, plainclothes police at the airport police station Liang, Jo, named Ma at the back of the group of gold jewelry. Identified, Liang at the back of the jewelry are gold jewelry, 13599.1 grams total weight, worth more than 2.89 million yuan; in Jo, named Ma, respectively, at the back of gold jewelry worth 100,000 yuan and 60,000 yuan.
Police qualitative suspicion of theft

Prosecutors believe that is wrong

Currently, the most controversial case of Liang Liang is charged with embezzlement or illegal to theft prosecution. The difference is huge. For the purpose of illegal possession, illegal materials will be forgotten by others, for himself, a relatively large amount, refuse to hand over the behavior constitutes illegal embezzlement, the maximum sentence is imprisonment for 5 years; and illegal possession for the purpose of the secret stolen large amounts of public and private property, constitutes theft, the maximum sentence is life imprisonment or even death.
Shenzhen Public Security Bureau after the end of the investigation, on suspicion of theft Liang case transferred to Shenzhen People's Procuratorate for examination and prosecution. Shenzhen Municipal People's Procuratorate, investigators believe that theft is wrong to prosecute, then the transfer of Bao'an District, Shenzhen People's Procuratorate for examination and prosecution. The Baoan District Prosecutor's Office investigators still tend Liang suspected of theft. Now the case has been sent back to the public security organ for supplementary investigation.
Therefore, the incident has been a full five months, Liang still not been prosecuted.
Liang husband:

cleaners can often pick up the items on board aircraft

Liu Jianhua, Liang and her husband are Kaifeng, Henan, their son this year Shenzhen third grade. In the eyes of Liu Jianhua, Liang was not a petty person. The incident two weeks ago, Liang had also picked up a briefcase, there are many documents and RMB, and she rushed to the business center, returned to the owner.
said Liu Jianhua, a detail, a cleaner at the airport is often picking up some of the items on the plane with no home use, often picked up some fruit, cosmetics, beverages, and so on.
Liang workers, a cleaner folks confirmed that they did pick up some of the unwanted things will go home, because the clean up of these discards is the responsibility of cleaning.
Experts:

Liang case can be written legal textbooks

Shenzhen University Law School professor Dr. Wu Xuebin said, the case can be written into the law books Liang . The focus of the case, if that act according to Liang to punish theft, it is entirely possible Liang was sentenced to life imprisonment, which is in violation of criminal law consistent with the principles of criminal culpability? Is contrary to the doctrine of responsibility in criminal law? However, if you do not act as a theft Liang treatment, the same feelings of simple people find it difficult to accept, in particular her gold jewelry will be picked up by the back of his own rented room.
Wu Xuebin that Liang's behavior is suspected of embezzlement, and not as a theft. Liang Xu Ting's case and the emergence of development and, ultimately, judicial process, for the habit of thinking subversive sense of justice.追问您的回答属于无意义灌水，已被举报

P(3+√2/2, 1-根2/2)
y=-3x-8-2根2追问详细过程

参考资料：高考完就没碰过数学了，参考下。

1.根据三角形相似的原理，AP:AB=1:√2时，过P点并平行于BC的直线才能把△ABC的面积分成相等的两部分.
2.根据1，可以求出P点的坐标.
3.由于PQ//BC，求出BC的斜率,也就求出了PQ的斜率.代入P点,容易求出PQ的直线方程.