軸對(duì)稱與坐標(biāo)變化 省賽獲獎(jiǎng)

第三章位置與坐標(biāo)3.軸對(duì)稱與坐標(biāo)變化一、學(xué)習(xí)目標(biāo)在平面直角坐標(biāo)系中：1.了解關(guān)于x軸對(duì)稱的兩點(diǎn)的特征2.了解關(guān)于y軸對(duì)稱的兩點(diǎn)的特征3.了解關(guān)于中心對(duì)稱的兩點(diǎn)的特征如果一個(gè)圖形沿著一條直線對(duì)折后兩部分完全重合，這樣的圖形叫做軸對(duì)稱圖形二、復(fù)習(xí)回顧1.什么叫軸對(duì)稱圖形？2.互為相反數(shù)的兩個(gè)數(shù)有什么特征？（1）互為相反數(shù)的兩個(gè)數(shù)相加之和等于0；（2）互為相反數(shù)的兩個(gè)數(shù)，數(shù)字一樣但符合相反。1.在如圖所示的平面直角坐標(biāo)系中，第一、二象限內(nèi)各有一面小旗。兩面小旗之間有怎樣的位置關(guān)系？對(duì)應(yīng)點(diǎn)A與A1的坐標(biāo)又有什么特點(diǎn)？其它對(duì)應(yīng)的點(diǎn)也有這個(gè)特點(diǎn)嗎？三、活動(dòng)探究3.做出這個(gè)點(diǎn)關(guān)于y軸對(duì)稱呢？2.在右邊的坐標(biāo)系內(nèi)，任取一點(diǎn)，做出這個(gè)點(diǎn)關(guān)于y軸對(duì)稱的點(diǎn)，看看兩個(gè)點(diǎn)的坐標(biāo)有什么樣的位置關(guān)系，說(shuō)說(shuō)其中的道理。123456780–1–2–3–4–512349105在直角坐標(biāo)系中描出以下各點(diǎn)：(0,0)(5,4)(3,0)(5,1)(5,-1)(3,0)(4,-2)(0,0)并用線段依次連接,看一看是什么圖案. yx12345-1-2-30–1–2–3–4–51234-4-55圖中的魚是將坐標(biāo)為：(0,0)(5,4)(3,0)(5,1)(5,-1)(3,0)(4,-2)(0,0)的點(diǎn)用線段依次連接而成的。yx兩個(gè)圖形關(guān)于y軸對(duì)稱要得到兩個(gè)關(guān)于y軸對(duì)稱的圖形：將各坐標(biāo)的縱坐標(biāo)保持不變，橫坐標(biāo)都乘以－１。頂點(diǎn)坐標(biāo)的變化：(x,y)(0,0)(5,4)(3,0)(5,1)(5,-1)(3,0)(4,-2)(0,0)(-x,y)(0,0)(-5,4)(-3,0)(-5,1)(-5,-1)(-3,0)(-4,-2)(0,0)觀察坐標(biāo)系中的兩條魚的位置關(guān)系？1、關(guān)于y軸對(duì)稱的兩個(gè)圖形上點(diǎn)的坐標(biāo)特征：(x,y)(-x,y)123456780–1–2–3–4–512345圖中的魚是將坐標(biāo)為：(0,0)(5,4)(3,0)(5,1)(5,-1)(3,0)(4,-2)(0,0)的點(diǎn)用線段依次連接而成的

將各坐標(biāo)的縱坐標(biāo)都乘以－1，橫坐標(biāo)保持不變，則圖形怎么變化？坐標(biāo)變化為：yx猜一猜與原圖形關(guān)于x軸對(duì)稱(x,y)(0,0)(5,4)(3,0)(5,1)(5,-1)(3,0)(4,-2)(0,0)(x,-y)(0,0)(5,-4)(3,0)(5,-1)(5,1)(3,0)(4,2)(0,0)1、關(guān)于y軸對(duì)稱的兩個(gè)圖形上點(diǎn)的坐標(biāo)特征：(x,y)(-x,y)2、關(guān)于x軸對(duì)稱的兩個(gè)圖形上點(diǎn)的坐標(biāo)特征：(x,y)(x,-y)–5

圖中的魚是將坐標(biāo)為：(0,0)(5,4)(3,0)(5,1)(5,-1)(3,0)(4,-2)(0,0)的點(diǎn)用線段依次連接而成的。

將各坐標(biāo)的縱坐標(biāo)與橫坐標(biāo)都乘以－1，圖形會(huì)變成什么樣？yx234510–1–2–3–412345–1–2–3–4–5坐標(biāo)變化為：猜想與原圖形關(guān)于原點(diǎn)中心對(duì)稱(x,y)(0,0)(5,4)(3,0)(5,1)(5,-1)(3,0)(4,-2)(0,0)(-x,-y)(0,0)(-5,-4)(-3,0)(-5,-1)(-5,1)(-3,0)(-4,2)(0,0)1、關(guān)于y軸對(duì)稱的兩個(gè)圖形上點(diǎn)的坐標(biāo)特征：(x,y)(-x,y)2、關(guān)于x軸對(duì)稱的兩個(gè)圖形上點(diǎn)的坐標(biāo)特征：(x,y)(x,-y)3、關(guān)于原點(diǎn)軸對(duì)稱的兩個(gè)圖形上點(diǎn)的坐標(biāo)特征：(x,y)(-x,-y)四、拓展練習(xí)1.點(diǎn)A（2，-3）關(guān)于x軸對(duì)稱的點(diǎn)的坐標(biāo)是（）.

2.點(diǎn)B（-2，1）關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)是（）.

3.點(diǎn)（4，3）與點(diǎn)（4，-3）的關(guān)系是（）.

A.關(guān)于原點(diǎn)對(duì)稱B.關(guān)于x軸對(duì)稱

C.關(guān)于y軸對(duì)稱D.不能構(gòu)成對(duì)稱關(guān)系

4.點(diǎn)（m，-1）和點(diǎn)（2，n）關(guān)于x軸對(duì)稱，則mn等于()

A.-2B.2C.1D.-1

1、關(guān)于y軸對(duì)稱的兩個(gè)圖形上點(diǎn)的坐標(biāo)特征：(x,y)(-x,y)2、關(guān)于x軸對(duì)稱的兩個(gè)圖形上點(diǎn)的坐標(biāo)特征：(x,y)(x,-y)3、關(guān)于原點(diǎn)軸對(duì)稱的兩個(gè)圖形上點(diǎn)的坐標(biāo)特征：(x,y)(-x,-y)五、歸納小結(jié)縱坐標(biāo)相同，橫坐標(biāo)互為相反數(shù)橫坐標(biāo)相同，縱坐標(biāo)互為相反數(shù)縱坐標(biāo)和橫坐標(biāo)都互為相反數(shù)六