题干

如图所示,△ABC中,已知顶点A(3,﹣1),∠B的内角平分线方程是x﹣4y+10=0过点C的中线方程为6x+10y﹣59=0.求顶点B的坐标和直线BC的方程.

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答案(点此获取答案解析)

解:设B(a,b),由过点B的角平分线方程x﹣4y+10=0得

a﹣4b+10=0,①

又AB中点( a+32,b

同类题2

阅读下面文言文,按要求回答问题。

【甲】愚公移山(节选)

    太行、王屋二山,方七百里,高万仞。本在冀州之南,河阳之北。

    北山愚公者,年且九十,面山而居。惩山北之塞,出入之迂也,聚室而谋曰:“吾与汝毕力平险,指通豫南,达于汉阴,可乎?”杂然相许。其妻献疑曰:“以君之力,曾不能损魁父之丘,如太行、王屋何?且焉置土石?”杂曰:“投诸渤海之尾,隐土之北。”遂率子孙荷担者三夫,叩石垦壤,箕畚运于渤海之尾。邻人京城氏之孀妻有遗男,始龀,跳往助之。寒暑易节,始一反焉。

【乙】卖蒜老叟

    南阳杨二相公精于拳术,每至演武场传授枪棒,观者如堵。一日,有卖蒜叟,咳嗽不绝声,旁睨而揶揄之。杨大怒,招叟至前,以拳打砖墙,陷入尺许,傲之曰:“叟能如是乎?”叟曰:“君能打墙,不能打人。”杨骂曰:“老奴能受我打乎?打死勿怨!”叟笑曰:“垂死之年,能以一死成君之名,死亦何怨!”老人自缚于树,解衣露腹。杨故取势于十步外,奋拳击之。老人寂然无声,但见杨双膝跪地,叩头曰:“晚生知罪矣。”拔其拳已夹入老人腹中坚不可出。哀求良久,老人鼓腹纵之,已跌出一石桥外矣。老人徐徐负蒜而归,卒不肯告人姓氏。

【注】①睨:眼睛斜着看。②揶揄:出言嘲笑、讽刺。

同类题5

阅读下面短文,从短文后的五个选项中选出能填入空白处的最佳选项。每个选项只能用一次。

    Is there anything worse than that? You bravely raise your hand to answer a question, but your teacher just point out that you’re wrong. What a shame! What could the teacher make you suffer (忍受) this?

    Relax. ____. Your teacher isn't calling you out to humiliate (使丢脸) you, but rather out of concern for you and your education.

    Having all your classmates come to know your weak points can be pretty hard, so how can you get past the shame and recognize class participation as a learning opportunity?

    Get out of your comfort zone. Terrill Schumaker, a teacher, explains that “the more you speak out, the more you learn how to grow and build confidence. ____

    Realize it's not a big deal. ____. People aren’t going to care all that much. “If I'm wrong or make a stupid point, then people laugh at me, but life moves on” says Grade 12 Kristen Wesenberg. Besides, everybody makes mistakes, and you can't be perfect all the time.

    ____. Of course it takes courage (勇气), but as Wesenberg says, ―What's the point of living in fear?‖ You won't learn anything if you are not brave enough.

    Use the experience as a learning tool. Wesenberg advises asking teachers why you're wrong so they can explain and you can learn.____. If you're wrong now, at least you won't be wrong in your next test!

A. Be brave in class

B. Trust your teacher instead

C. Use class time as a mini—test

D. And it's not the end of the world

E. Then you can live an exciting life