在所給的8×8的正方形網(wǎng)格中，按下列要求操作：（單位正方形邊長為1）
（1）請?jiān)诘诙笙迌?nèi)的格點(diǎn)上找一點(diǎn)C，使△ABC是以AB為底的等腰三角形，且腰長為無理數(shù)，試寫出C點(diǎn)的坐標(biāo)；
（2）畫出△ABC以點(diǎn)C為中心，旋轉(zhuǎn)180°后的△A′B′C′，并求△A′B′C′的面積．

【答案】分析：（1）要等腰，可見頂點(diǎn)要在底的垂直平分線上，要腰長為無理數(shù)，則腰長要是網(wǎng)格的對角線．依此找點(diǎn)就可，答案不唯一．
（2）將△ABC的各頂點(diǎn)繞點(diǎn)C旋轉(zhuǎn)180°后，找到對應(yīng)點(diǎn)，順次連接得到的△A'B'C．
解答：解：（1）如圖所示：
腰AC的長．
∴C點(diǎn)坐標(biāo)為：（-1，1）；

（2）△A′B′C′的面積=△ABC的面積，
∴△A′B′C′的面積=×2×2=4．
點(diǎn)評：本題考查了網(wǎng)格的應(yīng)用，及對無理數(shù)的理解，主要考查的還是旋轉(zhuǎn)作圖的作法，但又綜合了三角形面積的求解．
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