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    精英家教网 > 初中数学 > 题目详情
    在所给的8×8的正方形网格中，按下列要求操作：（单位正方形边长为1）
    （1）请在第二象限内的格点上找一点C，使△ABC是以AB为底的等腰三角形，且腰长为无理数，试写出C点的坐标；
    （2）画出△ABC以点C为中心，旋转180°后的△A′B′C′，并求△A′B′C′的面积．

    【答案】分析：（1）要等腰，可见顶点要在底的垂直平分线上，要腰长为无理数，则腰长要是网格的对角线．依此找点就可，答案不唯一．
    （2）将△ABC的各顶点绕点C旋转180°后，找到对应点，顺次连接得到的△A'B'C．
    解答：解：（1）如图所示：
    腰AC的长．
    ∴C点坐标为：（-1，1）；

    （2）△A′B′C′的面积=△ABC的面积，
    ∴△A′B′C′的面积=×2×2=4．
    点评：本题考查了网格的应用，及对无理数的理解，主要考查的还是旋转作图的作法，但又综合了三角形面积的求解．
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