Question

如圖，△ABC是格點(diǎn)三角形,且A（－3，－2），B（－2，－3），C（1，－1）．

（1）請(qǐng)?jiān)趫D中畫(huà)出△ABC關(guān)于y軸的對(duì)稱△A’B’C’．
（2）寫(xiě)出△A’B’C’各點(diǎn)坐標(biāo),并計(jì)算△A’B’C’的面積．

Answer 1

(1)作圖見(jiàn)解析;(2) △A’B’C’的面積=2.5.

試題分析：(1)要作出一個(gè)三角形關(guān)于y軸的對(duì)稱圖形,只需要作出三個(gè)頂點(diǎn)關(guān)于y軸對(duì)稱的對(duì)稱點(diǎn),然后連接這三個(gè)對(duì)稱點(diǎn)即可,如圖,過(guò)點(diǎn)A作y軸的垂線交y軸與點(diǎn)G,延長(zhǎng)AG至點(diǎn)A’,使得AG=" A’G," 點(diǎn)A’是點(diǎn)A關(guān)于y軸的對(duì)稱點(diǎn), 過(guò)點(diǎn)B作y軸的垂線交y軸與點(diǎn)I,延長(zhǎng)BI至點(diǎn)B’,使得BI=" B’I," 點(diǎn)B’是點(diǎn)B關(guān)于y軸的對(duì)稱點(diǎn), 過(guò)點(diǎn)C作y軸的垂線交y軸與點(diǎn)H,延長(zhǎng)CH至點(diǎn)C’,使得CH= C’H, 點(diǎn)C’是點(diǎn)C關(guān)于y軸的對(duì)稱點(diǎn),連接A’B’C’,得到圖形△A’B’C’; (2)將要求三角形放在一個(gè)矩形里面,三角形的面積等于矩形的面積減去三個(gè)直角三角形的面積,如圖,作矩形FE C’D,△A’B’C’的面積=矩形FE C’D的面積-△B’C’D的面積-△A’C’E-△A’B’F的面積=2×4-×2×3-×1×4-×1×1= 8-3-2-=2.5.
試題解析：

(1)如圖,過(guò)點(diǎn)A作y軸的垂線交y軸與點(diǎn)G,延長(zhǎng)AG至點(diǎn)A’,使得AG=" A’G," 點(diǎn)A’是點(diǎn)A關(guān)于y軸的對(duì)稱點(diǎn), 過(guò)點(diǎn)B作y軸的垂線交y軸與點(diǎn)I,延長(zhǎng)BI至點(diǎn)B’,使得BI=" B’I," 點(diǎn)B’是點(diǎn)B關(guān)于y軸的對(duì)稱點(diǎn), 過(guò)點(diǎn)C作y軸的垂線交y軸與點(diǎn)H,延長(zhǎng)CH至點(diǎn)C’,使得CH= C’H, 點(diǎn)C’是點(diǎn)C關(guān)于y軸的對(duì)稱點(diǎn),連接A’B’C’,得到圖形△A’B’C’.
(2)如圖,作矩形FE C’D,△A’B’C’的面積=矩形FE C’D的面積-△B’C’D的面積-△A’C’E-△A’B’F的面積=2×4-×2×3-×1×4-×1×1= 8-3-2-=2.5.