我們發(fā)現(xiàn)當(dāng)圖形平移時,圖形的形狀、大小都不變,只是位置變了.但是圖形橫向、縱向伸縮后.形狀和大小都發(fā)生了變化,下面我們從面積的變化來感受一下這種變化.首先在平面直角坐標系中畫出長方形ABCD(如下圖),其
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各點的坐標分別為A(1,2),B(1,-1),C(6,-1),D(6,2),則AB=
,BC=
,S
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=_____.
(1)將各點的橫坐標不變,縱坐標都乘以2,并把所得各點依次連結(jié),得到長方形A
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B
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C
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D
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,A
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(1,4), B
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(1,-2), C
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(6,-2),
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D
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(6,4),則A
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B
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=_____B
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C
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=
,S
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=_____.顯然S
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=2 S
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,
即圖形縱向拉長為原來的2倍,面積也變?yōu)樵瓉淼?倍.
(2)很顯然,若將原長方形ABCD縱向縮為原來的
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,面積也就會變?yōu)樵瓉淼?IMG style="WIDTH: 16px; HEIGHT: 37px; VERTICAL-ALIGN: middle" src="http://thumb.zyjl.cn/pic1/upload/papers/c02/20120722/20120722165037577566.png">.
橫向伸縮(縱向不變)的變化規(guī)律與此相同.
(3)探究:若將長方形ABCD各點的橫坐標都乘以2,縱坐標都乘以3,則所得長方形的面積是原長方形ABCD面積的____________倍
(4)若將原長方形ABCD各點的橫坐標都乘以m,縱坐標都乘以n(m、n均為正數(shù)),則所得長方形的面積是原長方形ABCD面積的____________倍;若m、n中有負數(shù)時,面積的變化規(guī)律如何?(注:變化規(guī)律按照同學(xué)的語言寫對意思即可)