题干

如图,直线l1在平面直角坐标系中,直线l1与y轴交于点A,点B(﹣3,3)也在直线l1上,将点B先向右平移1个单位长度,再向下平移2个单位长度得到点C,点C恰好也在直线l1上.

(1)求点C的坐标和直线l1的解析式;

(2)若将点C先向左平移3个单位长度,再向上平移6个单位长度得到点D,请你判断点D是否在直线l1上;

(3)已知直线l2:y=x+b经过点B,与y轴交于点E,求△ABE的面积.

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答案(点此获取答案解析)

解:(1)∵B(﹣3,3),将点B先向右平移1个单位长度,再向下平移2个单位长度得到点C,

∴﹣3+1=﹣2,3﹣2=1,

∴C的坐标为(﹣2,1),

设直线l1的解析式为y=kx+c,

∵点B、C在直线l1上,

∴代入得:

同类题4

阅读下面短文,从短文后所给的A、B、C、D四个选项中, 选出可以填入空白处的最佳选项

    “It's nice having a friend,” said Mole (鼹鼠) to Rabbit as they sat talking in the sun one day.

    “Oh, it is!” said Rabbit.“Very useful, too, 1 if you need help. 2, I think I'd like Bull(公牛) to be my friend.”

    “But I'm your friend!” said Mole, feeling 3.

    “Oh, yes,” said Rabbit.“You are good for talking to and laughing with, 4you are too small. When I need help, I 5 someone big and strong like Bull.He would be a very good friend to have. It would be 6 shouting for him when I need help.”

    Mole went off in anger.

    “Oh,well,I need to 7 something,” Rabbit thought.

    He moved along 8 he found a tiny garden.He had just started on his first leaf when there was a big 9. People were shouting and dogs were barking(吠叫).Rabbit was so afraid and in such a 10 to get away that he ran into the wrong hole.

    The hole was too 11 and Rabbit got stuck(被卡住).He could not 12 at all.

    “Help!” cried Rabbit.

    Mole 13 him.He ran up to see what was the matter.

    “Help!” cried Rabbit.“I'm stuck in this hole.”

    “If you want help,” said Mole,“I'd better 14 Bull.”

    “No!” cried Rabbit.“He's no good! He's too big to get into this 15.You're just the right 16! Please help me,Mole!”

    So Mole began digging around Rabbit.He 17 so fast that Rabbit was 18 soon.

    “I'm sorry, Mole.I was 19,” Rabbit said.“I'm 20 I have you for a friend.” And so the two good friends set off for home together.