问题 问答题

In the rectangular coordinate system above, the line y=x is the perpendicular bisector of segment AB (not shown), and the x-axis is the perpendicular bisector of segment BC (not shown). If the coordinates of point A are (2, 3), what are the coordinates of point C ?

答案

参考答案:

(3, -2)

解析:

直线y=x垂直平分线段AB,也即A点和B点关于直线对称,所以B点的纵坐标等于A点的横坐标,B点的横坐标等于A点的纵坐标,即B点的坐标为(3, 2);同理C点和B点关于x轴对称,因此B点与C点的x坐标一样,而纵坐标则互为相反数,所以C点的坐标为(3, -2)

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