如图,点A的坐标为(-1,0),点B在直线y=x上运动,当线段AB最短时,点

如图,点A的坐标为(-1,0),点B在直线y=x上运动,当线段AB最短时,点B的坐标为_________。

答案

解析:
:过A点作垂直于直线y=x的垂线AB,
∵点B在直线y=x上运动,
∴∠AOB=45°,
∴△AOB为等腰直角三角形,
过B作BC垂直x轴垂足为C,
则点C为OA的中点,
则OC=BC=
作图可知B在x下方,y的右方.
∴横坐标负,纵坐标为负.
所以当线段AB最短时,点B的坐标为(-,-).

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