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1、小專題(六)坐標(biāo)系中的軸對(duì)稱變換類型1關(guān)于坐標(biāo)軸對(duì)稱的點(diǎn)的坐標(biāo)方法歸納:關(guān)于x軸對(duì)稱時(shí),橫坐標(biāo)不變,縱坐標(biāo)互為相反數(shù);關(guān)于y軸對(duì)稱時(shí),橫坐標(biāo)互為相反數(shù),縱坐標(biāo)不變1點(diǎn)(5,3)關(guān)于x軸對(duì)稱的點(diǎn)的坐標(biāo)是_2點(diǎn)(3,5)關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)是_3已知A(a,5),B(2,b)兩點(diǎn)關(guān)于x軸對(duì)稱,則a_,b_4若點(diǎn)P關(guān)于y軸的對(duì)稱點(diǎn)為P(2,3),則點(diǎn)P關(guān)于x軸對(duì)稱的點(diǎn)的坐標(biāo)是_(5,3)(3,5)25(2,3)5已知點(diǎn)M(2ab,5a),N(2b1,ab)(1)若點(diǎn)M,N關(guān)于x軸對(duì)稱,求a、b的值;(2)若點(diǎn)M,N關(guān)于y軸對(duì)稱,求(4ab)2016的值6如圖所示,在平面直角坐標(biāo)系xOy中,A(1,
2、5),B(1,0),C(4,3),直線m為橫坐標(biāo)都為2的點(diǎn)組成的一條直線(1)作出ABC關(guān)于直線m對(duì)稱的A1B1C1;(2)直接寫出A1,B1,C1的坐標(biāo);(3)求出A1B1C1的面積圖略A1(5,5),B1(5,0),C1(8,3)A1B1C1的面積為7.5.類型2關(guān)于平行于坐標(biāo)軸的直線對(duì)稱的點(diǎn)的坐標(biāo)方法歸納:關(guān)于平行于x軸的直線對(duì)稱時(shí),橫坐標(biāo)不變,縱坐標(biāo)之和等于對(duì)稱軸縱坐標(biāo)的2倍;關(guān)于平行于y軸的直線對(duì)稱時(shí),橫坐標(biāo)之和等于對(duì)稱軸橫坐標(biāo)的2倍,縱坐標(biāo)不變7已知(如圖所示)A(3,2),B(3,4),C(4,2),D(2,2)(1)A與B是對(duì)稱點(diǎn)嗎?如果是對(duì)稱點(diǎn),對(duì)稱軸是什么?畫出對(duì)稱軸;A與
3、B是對(duì)稱點(diǎn),對(duì)稱軸是直線y3,圖略(2)C與D是對(duì)稱點(diǎn)嗎?如果是對(duì)稱點(diǎn),對(duì)稱軸是什么?畫出對(duì)稱軸;(3)已知點(diǎn)M(1,3),寫出它關(guān)于x2對(duì)稱的點(diǎn)N的坐標(biāo)和它關(guān)于直線y1對(duì)稱的點(diǎn)Q的坐標(biāo)C與D是對(duì)稱點(diǎn),對(duì)稱軸是直線x1,圖略點(diǎn)M(1,3)關(guān)于x2對(duì)稱的點(diǎn)N的坐標(biāo)為(5,3),關(guān)于直線y1對(duì)稱的點(diǎn)Q的坐標(biāo)(1,5)8已知點(diǎn)A1(2,5)關(guān)于y軸的對(duì)稱點(diǎn)是A2,關(guān)于原點(diǎn)的對(duì)稱點(diǎn)是A3.(1)求A1A2A3的面積;(2)如果將A1A2A3沿著直線y5翻折可得到B1B2B3,請(qǐng)寫出B1,B2,B3的坐標(biāo)點(diǎn)A1(2,5)關(guān)于y5對(duì)稱的點(diǎn)B1的坐標(biāo)為(2,15);點(diǎn)A2(2,5)關(guān)于y5對(duì)稱的點(diǎn)B2的坐標(biāo)
4、為(2,15);點(diǎn)A3(2,5)關(guān)于y5對(duì)稱的點(diǎn)B3的坐標(biāo)為(2,5)類型3關(guān)于第一、三象限角平分線對(duì)稱的點(diǎn)的坐標(biāo)方法歸納:點(diǎn)P(m,n)關(guān)于第一、三象限角平分線對(duì)稱點(diǎn)的坐標(biāo)為(n,m);點(diǎn)P(m,n)關(guān)于第二、四象限角平分線對(duì)稱點(diǎn)的坐標(biāo)為(n,m)9如圖,在平面直角系中,直線l是第一、三象限的角平分線實(shí)驗(yàn)探究:由圖觀察知A(0,2)關(guān)于直線l的對(duì)稱點(diǎn)A的坐標(biāo)為(2,0),請(qǐng)?jiān)趫D中分別標(biāo)明B(5,3)、C(2,5)關(guān)于直線l的對(duì)稱點(diǎn)B、C的位置,并寫出它們的坐標(biāo):B_、C_;(3,5)(5,2)歸納與發(fā)現(xiàn):結(jié)合圖形觀察以上三組點(diǎn)的坐標(biāo),你會(huì)發(fā)現(xiàn):坐標(biāo)平面內(nèi)任一點(diǎn)P(m,n)關(guān)于第一、三象限的角平分線l的對(duì)稱點(diǎn)P的坐標(biāo)為_(kāi)(n,m)圖略10綜合平面直角坐標(biāo)系,解答下列問(wèn)題:(1)點(diǎn)(3,4)和點(diǎn)(4,3)是否關(guān)于第一、三象限兩坐標(biāo)軸夾角的平分線對(duì)稱?如圖:點(diǎn)(3,4)和點(diǎn)(4,3)關(guān)于第一、三象限兩坐標(biāo)軸夾角的平分線對(duì)稱(2)點(diǎn)(3,4)和點(diǎn)(4,3)是否關(guān)于第二、四象限兩坐標(biāo)軸夾角的平分線對(duì)稱?點(diǎn)(3,4)和點(diǎn)(4,3)關(guān)于第二、四象限兩坐標(biāo)軸夾角的平分線對(duì)稱