人教版第13章 軸對(duì)稱測(cè)試卷(2)
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人教版第13章 軸對(duì)稱 測(cè)試卷(2) 一、選擇題 1.在平面直角坐標(biāo)系中,點(diǎn)A(﹣1,2)關(guān)于x軸對(duì)稱的點(diǎn)B的坐標(biāo)為( ?。? A.(﹣1,2) B.(1,2) C.(1,﹣2) D.(﹣1,﹣2) 2.如圖,△ABC與△DEF關(guān)于y軸對(duì)稱,已知A(﹣4,6),B(﹣6,2),E(2,1),則點(diǎn)D的坐標(biāo)為( ?。? A.(﹣4,6) B.(4,6) C.(﹣2,1) D.(6,2) 3.在平面直角坐標(biāo)系中,與點(diǎn)(1,2)關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)是( ?。? A.(﹣1,2) B.(1,﹣2) C.(﹣1,﹣2) D.(﹣2,﹣1) 4.點(diǎn)(3,2)關(guān)于x軸的對(duì)稱點(diǎn)為( ?。? A.(3,﹣2) B.(﹣3,2) C.(﹣3,﹣2) D.(2,﹣3) 5.在平面直角坐標(biāo)系中,點(diǎn)P(﹣3,2)關(guān)于直線y=x對(duì)稱點(diǎn)的坐標(biāo)是( ?。? A.(﹣3,﹣2) B.(3,2) C.(2,﹣3) D.(3,﹣2) 6.在平面直角坐標(biāo)系中,已知點(diǎn)A(2,3),則點(diǎn)A關(guān)于x軸的對(duì)稱點(diǎn)的坐標(biāo)為( ?。? A.(3,2) B.(2,﹣3) C.(﹣2,3) D.(﹣2,﹣3) 7.點(diǎn)P(2,﹣5)關(guān)于x軸對(duì)稱的點(diǎn)的坐標(biāo)為( ?。? A.(﹣2,5) B.(2,5) C.(﹣2,﹣5) D.(2,﹣5) 8.點(diǎn)A(1,﹣2)關(guān)于x軸對(duì)稱的點(diǎn)的坐標(biāo)是( ?。? A.(1,﹣2) B.(﹣1,2) C.(﹣1,﹣2) D.(1,2) 9.已知點(diǎn)A(a,2013)與點(diǎn)B(2014,b)關(guān)于x軸對(duì)稱,則a+b的值為( ) A.﹣1 B.1 C.2 D.3 二、填空題 10.平面直角坐標(biāo)系中,點(diǎn)A(2,0)關(guān)于y軸對(duì)稱的點(diǎn)A′的坐標(biāo)為 ?。? 11.在平面直角坐標(biāo)系中,點(diǎn)A的坐標(biāo)是(2,﹣3),作點(diǎn)A關(guān)于x軸的對(duì)稱點(diǎn),得到點(diǎn)A′,再作點(diǎn)A′關(guān)于y軸的對(duì)稱點(diǎn),得到點(diǎn)A″,則點(diǎn)A″的坐標(biāo)是( , ?。? 12.在平面直角坐標(biāo)系中,點(diǎn)(﹣3,2)關(guān)于y軸的對(duì)稱點(diǎn)的坐標(biāo)是 ?。? 13.已知點(diǎn)P(3,a)關(guān)于y軸的對(duì)稱點(diǎn)為Q(b,2),則ab= ?。? 14.若點(diǎn)M(3,a)關(guān)于y軸的對(duì)稱點(diǎn)是點(diǎn)N(b,2),則(a+b)2014= ?。? 15.已知點(diǎn)P(3,﹣1)關(guān)于y軸的對(duì)稱點(diǎn)Q的坐標(biāo)是(a+b,1﹣b),則ab的值為 ?。? 16.點(diǎn)A(﹣3,0)關(guān)于y軸的對(duì)稱點(diǎn)的坐標(biāo)是 . 17.點(diǎn)P(2,﹣1)關(guān)于x軸對(duì)稱的點(diǎn)P′的坐標(biāo)是 ?。? 18.在平面直角坐標(biāo)系中,點(diǎn)A(2,﹣3)關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)為 ?。? 19.點(diǎn)P(﹣2,3)關(guān)于x軸的對(duì)稱點(diǎn)P′的坐標(biāo)為 ?。? 20.點(diǎn)P(3,2)關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)是 ?。? 21.點(diǎn)P(1,﹣2)關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)為 ?。? 22.點(diǎn)A(﹣3,2)關(guān)于x軸的對(duì)稱點(diǎn)A′的坐標(biāo)為 ?。? 23.若點(diǎn)A(m+2,3)與點(diǎn)B(﹣4,n+5)關(guān)于y軸對(duì)稱,則m+n= ?。? 24.點(diǎn)P(2,3)關(guān)于x軸的對(duì)稱點(diǎn)的坐標(biāo)為 ?。? 25.已知P(1,﹣2),則點(diǎn)P關(guān)于x軸的對(duì)稱點(diǎn)的坐標(biāo)是 ?。? 三、解答題 26.在如圖所示的直角坐標(biāo)系中,每個(gè)小方格都是邊長(zhǎng)為1的正方形,△ABC的頂點(diǎn)均在格點(diǎn)上,點(diǎn)A的坐標(biāo)是(﹣3,﹣1). (1)將△ABC沿y軸正方向平移3個(gè)單位得到△A1B1C1,畫(huà)出△A1B1C1,并寫(xiě)出點(diǎn)B1坐標(biāo); (2)畫(huà)出△A1B1C1關(guān)于y軸對(duì)稱的△A2B2C2,并寫(xiě)出點(diǎn)C2的坐標(biāo). 27.如圖,在邊長(zhǎng)為1個(gè)單位長(zhǎng)度的小正方形網(wǎng)格中,給出了△ABC(頂點(diǎn)是網(wǎng)格線的交點(diǎn)). (1)請(qǐng)畫(huà)出△ABC關(guān)于直線l對(duì)稱的△A1B1C1; (2)將線段AC向左平移3個(gè)單位,再向下平移5個(gè)單位,畫(huà)出平移得到的線段A2C2,并以它為一邊作一個(gè)格點(diǎn)△A2B2C2,使A2B2=C2B2. 28.在平面直角坐標(biāo)系中,△ABC的頂點(diǎn)坐標(biāo)A(﹣4,1),B(﹣2,1),C(﹣2,3) (1)作△ABC關(guān)于y軸的對(duì)稱圖形△A1B1C1; (2)將△ABC向下平移4個(gè)單位長(zhǎng)度,作出平移后的△A2B2C2; (3)求四邊形AA2B2C的面積. 29.在平面直角坐標(biāo)系中,已知點(diǎn)A(﹣3,1),B(﹣1,0),C(﹣2,﹣1),請(qǐng)?jiān)趫D中畫(huà)出△ABC,并畫(huà)出與△ABC關(guān)于y軸對(duì)稱的圖形. 30.如圖,△ABC與△DEF關(guān)于直線l對(duì)稱,請(qǐng)僅用無(wú)刻度的直尺,在下面兩個(gè)圖中分別作出直線l. 參考答案與試題解析 一、選擇題 1.在平面直角坐標(biāo)系中,點(diǎn)A(﹣1,2)關(guān)于x軸對(duì)稱的點(diǎn)B的坐標(biāo)為( ?。? A.(﹣1,2) B.(1,2) C.(1,﹣2) D.(﹣1,﹣2) 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)關(guān)于x軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn):橫坐標(biāo)不變,縱坐標(biāo)互為相反數(shù)可得B點(diǎn)坐標(biāo). 【解答】解:點(diǎn)A(﹣1,2)關(guān)于x軸對(duì)稱的點(diǎn)B的坐標(biāo)為(﹣1,﹣2), 故選:D. 【點(diǎn)評(píng)】此題主要考查了關(guān)于x軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn),關(guān)鍵是掌握點(diǎn)的坐標(biāo)的變化規(guī)律. 2.如圖,△ABC與△DEF關(guān)于y軸對(duì)稱,已知A(﹣4,6),B(﹣6,2),E(2,1),則點(diǎn)D的坐標(biāo)為( ) A.(﹣4,6) B.(4,6) C.(﹣2,1) D.(6,2) 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)關(guān)于y軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn):橫坐標(biāo)互為相反數(shù),縱坐標(biāo)不變.即點(diǎn)P(x,y)關(guān)于y軸的對(duì)稱點(diǎn)P′的坐標(biāo)是(﹣x,y),進(jìn)而得出答案. 【解答】解:∵△ABC與△DEF關(guān)于y軸對(duì)稱,A(﹣4,6), ∴D(4,6). 故選:B. 【點(diǎn)評(píng)】此題主要考查了關(guān)于y軸對(duì)稱點(diǎn)的性質(zhì),準(zhǔn)確記憶橫縱坐標(biāo)的關(guān)系是解題關(guān)鍵. 3.在平面直角坐標(biāo)系中,與點(diǎn)(1,2)關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)是( ?。? A.(﹣1,2) B.(1,﹣2) C.(﹣1,﹣2) D.(﹣2,﹣1) 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)“關(guān)于y軸對(duì)稱的點(diǎn),縱坐標(biāo)相同,橫坐標(biāo)互為相反數(shù)”解答即可. 【解答】解:點(diǎn)(1,2)關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)是(﹣1,2). 故選A. 【點(diǎn)評(píng)】解決本題的關(guān)鍵是掌握好對(duì)稱點(diǎn)的坐標(biāo)規(guī)律: (1)關(guān)于x軸對(duì)稱的點(diǎn),橫坐標(biāo)相同,縱坐標(biāo)互為相反數(shù); (2)關(guān)于y軸對(duì)稱的點(diǎn),縱坐標(biāo)相同,橫坐標(biāo)互為相反數(shù); (3)關(guān)于原點(diǎn)對(duì)稱的點(diǎn),橫坐標(biāo)與縱坐標(biāo)都互為相反數(shù). 4.點(diǎn)(3,2)關(guān)于x軸的對(duì)稱點(diǎn)為( ?。? A.(3,﹣2) B.(﹣3,2) C.(﹣3,﹣2) D.(2,﹣3) 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)關(guān)于x軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn):橫坐標(biāo)不變,縱坐標(biāo)互為相反數(shù)可直接寫(xiě)出答案. 【解答】解:點(diǎn)(3,2)關(guān)于x軸的對(duì)稱點(diǎn)為(3,﹣2), 故選:A. 【點(diǎn)評(píng)】此題主要考查了關(guān)于x軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn),關(guān)鍵是掌握點(diǎn)的坐標(biāo)的變化規(guī)律. 5.在平面直角坐標(biāo)系中,點(diǎn)P(﹣3,2)關(guān)于直線y=x對(duì)稱點(diǎn)的坐標(biāo)是( ?。? A.(﹣3,﹣2) B.(3,2) C.(2,﹣3) D.(3,﹣2) 【考點(diǎn)】坐標(biāo)與圖形變化-對(duì)稱. 【分析】根據(jù)直線y=x是第一、三象限的角平分線,和點(diǎn)P的坐標(biāo)結(jié)合圖形得到答案. 【解答】解:點(diǎn)P關(guān)于直線y=x對(duì)稱點(diǎn)為點(diǎn)Q, 作AP∥x軸交y=x于A, ∵y=x是第一、三象限的角平分線, ∴點(diǎn)A的坐標(biāo)為(2,2), ∵AP=AQ, ∴點(diǎn)Q的坐標(biāo)為(2,﹣3) 故選:C. 【點(diǎn)評(píng)】本題考查的是坐標(biāo)與圖形的變換,掌握軸對(duì)稱的性質(zhì)是解題的關(guān)鍵,注意角平分線的性質(zhì)的應(yīng)用. 6.在平面直角坐標(biāo)系中,已知點(diǎn)A(2,3),則點(diǎn)A關(guān)于x軸的對(duì)稱點(diǎn)的坐標(biāo)為( ?。? A.(3,2) B.(2,﹣3) C.(﹣2,3) D.(﹣2,﹣3) 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)關(guān)于x軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn):橫坐標(biāo)不變,縱坐標(biāo)互為相反數(shù).即點(diǎn)P(x,y)關(guān)于x軸的對(duì)稱點(diǎn)P′的坐標(biāo)是(x,﹣y),進(jìn)而得出答案. 【解答】解:∵點(diǎn)A(2,3), ∴點(diǎn)A關(guān)于x軸的對(duì)稱點(diǎn)的坐標(biāo)為:(2,﹣3). 故選:B. 【點(diǎn)評(píng)】此題主要考查了關(guān)于x軸對(duì)稱點(diǎn)的性質(zhì),正確記憶關(guān)于坐標(biāo)軸對(duì)稱點(diǎn)的性質(zhì)是解題關(guān)鍵. 7.點(diǎn)P(2,﹣5)關(guān)于x軸對(duì)稱的點(diǎn)的坐標(biāo)為( ?。? A.(﹣2,5) B.(2,5) C.(﹣2,﹣5) D.(2,﹣5) 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)關(guān)于x軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn):橫坐標(biāo)不變,縱坐標(biāo)互為相反數(shù).即點(diǎn)P(x,y)關(guān)于x軸的對(duì)稱點(diǎn)P′的坐標(biāo)是(x,﹣y),進(jìn)而得出答案. 【解答】解:∵點(diǎn)P(2,﹣5)關(guān)于x軸對(duì)稱, ∴對(duì)稱點(diǎn)的坐標(biāo)為:(2,5). 故選:B. 【點(diǎn)評(píng)】此題主要考查了關(guān)于x軸對(duì)稱點(diǎn)的坐標(biāo)性質(zhì),正確記憶坐標(biāo)變化規(guī)律是解題關(guān)鍵. 8.點(diǎn)A(1,﹣2)關(guān)于x軸對(duì)稱的點(diǎn)的坐標(biāo)是( ?。? A.(1,﹣2) B.(﹣1,2) C.(﹣1,﹣2) D.(1,2) 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)關(guān)于x軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn):橫坐標(biāo)不變,縱坐標(biāo)互為相反數(shù)可直接得到答案. 【解答】解:點(diǎn)A(1,﹣2)關(guān)于x軸對(duì)稱的點(diǎn)的坐標(biāo)是(1,2), 故選:D. 【點(diǎn)評(píng)】此題主要考查了關(guān)于x軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn),關(guān)鍵是掌握點(diǎn)的坐標(biāo)的變化規(guī)律. 9.已知點(diǎn)A(a,2013)與點(diǎn)B(2014,b)關(guān)于x軸對(duì)稱,則a+b的值為( ?。? A.﹣1 B.1 C.2 D.3 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)關(guān)于x軸對(duì)稱點(diǎn)的坐標(biāo)的特點(diǎn),可以得到點(diǎn)A的坐標(biāo)與點(diǎn)B的坐標(biāo)的關(guān)系. 【解答】解:∵A(a,2013)與點(diǎn)B(2014,b)關(guān)于x軸對(duì)稱, ∴a=2014,b=﹣2013 ∴a+b=1, 故選:B. 【點(diǎn)評(píng)】此題主要考查了關(guān)于x、y軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn),關(guān)鍵是掌握點(diǎn)的坐標(biāo)的變化規(guī)律. 二、填空題(共16小題) 10.平面直角坐標(biāo)系中,點(diǎn)A(2,0)關(guān)于y軸對(duì)稱的點(diǎn)A′的坐標(biāo)為?。ī?,0)?。? 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)關(guān)于y軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn):橫坐標(biāo)互為相反數(shù),縱坐標(biāo)不變可以直接寫(xiě)出答案. 【解答】解:點(diǎn)A(2,0)關(guān)于y軸對(duì)稱的點(diǎn)A′的坐標(biāo)為(﹣2,0), 故答案為:(﹣2,0). 【點(diǎn)評(píng)】此題主要考查了關(guān)于y軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn),關(guān)鍵是掌握點(diǎn)的坐標(biāo)的變化規(guī)律. 11.在平面直角坐標(biāo)系中,點(diǎn)A的坐標(biāo)是(2,﹣3),作點(diǎn)A關(guān)于x軸的對(duì)稱點(diǎn),得到點(diǎn)A′,再作點(diǎn)A′關(guān)于y軸的對(duì)稱點(diǎn),得到點(diǎn)A″,則點(diǎn)A″的坐標(biāo)是( ﹣2 , 3?。? 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】分別利用x軸、y軸對(duì)稱點(diǎn)的性質(zhì),得出A′,A″的坐標(biāo)進(jìn)而得出答案. 【解答】解:∵點(diǎn)A的坐標(biāo)是(2,﹣3),作點(diǎn)A關(guān)于x軸的對(duì)稱點(diǎn),得到點(diǎn)A′, ∴A′的坐標(biāo)為:(2,3), ∵點(diǎn)A′關(guān)于y軸的對(duì)稱點(diǎn),得到點(diǎn)A″, ∴點(diǎn)A″的坐標(biāo)是:(﹣2,3). 故答案為:﹣2;3. 【點(diǎn)評(píng)】此題主要考查了關(guān)于x軸、y軸對(duì)稱點(diǎn)的性質(zhì). (1)關(guān)于x軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn): 橫坐標(biāo)不變,縱坐標(biāo)互為相反數(shù). 即點(diǎn)P(x,y)關(guān)于x軸的對(duì)稱點(diǎn)P′的坐標(biāo)是(x,﹣y). (2)關(guān)于y軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn): 橫坐標(biāo)互為相反數(shù),縱坐標(biāo)不變. 即點(diǎn)P(x,y)關(guān)于y軸的對(duì)稱點(diǎn)P′的坐標(biāo)是(﹣x,y). 12.在平面直角坐標(biāo)系中,點(diǎn)(﹣3,2)關(guān)于y軸的對(duì)稱點(diǎn)的坐標(biāo)是?。?,2)?。? 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)關(guān)于y軸對(duì)稱的點(diǎn),縱坐標(biāo)相同,橫坐標(biāo)互為相反數(shù),可得答案. 【解答】解:在平面直角坐標(biāo)系中,點(diǎn)(﹣3,2)關(guān)于y軸的對(duì)稱點(diǎn)的坐標(biāo)是(3,2), 故答案為:(3,2). 【點(diǎn)評(píng)】本題考查了關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo),解決本題的關(guān)鍵是掌握好對(duì)稱點(diǎn)的坐標(biāo)規(guī)律:關(guān)于x軸對(duì)稱的點(diǎn),橫坐標(biāo)相同,縱坐標(biāo)互為相反數(shù);關(guān)于y軸對(duì)稱的點(diǎn),縱坐標(biāo)相同,橫坐標(biāo)互為相反數(shù);關(guān)于原點(diǎn)對(duì)稱的點(diǎn),橫坐標(biāo)與縱坐標(biāo)都互為相反數(shù). 13.已知點(diǎn)P(3,a)關(guān)于y軸的對(duì)稱點(diǎn)為Q(b,2),則ab= ﹣6?。? 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)關(guān)于y軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn):橫坐標(biāo)互為相反數(shù),縱坐標(biāo)不變可得a=2,b=﹣3,進(jìn)而可得答案. 【解答】解:∵點(diǎn)P(3,a)關(guān)于y軸的對(duì)稱點(diǎn)為Q(b,2), ∴a=2,b=﹣3, ∴ab=﹣6, 故答案為:﹣6. 【點(diǎn)評(píng)】此題主要考查了關(guān)于y軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn),關(guān)鍵是掌握點(diǎn)的坐標(biāo)的變化規(guī)律. 14.若點(diǎn)M(3,a)關(guān)于y軸的對(duì)稱點(diǎn)是點(diǎn)N(b,2),則(a+b)2014= 1?。? 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)軸對(duì)稱的性質(zhì),點(diǎn)M和點(diǎn)N的縱坐標(biāo)相等,橫坐標(biāo)互為相反數(shù),可以求得a、b的值,從而可得a+b的值. 【解答】解:∵點(diǎn)M(3,a)關(guān)于y軸的對(duì)稱點(diǎn)是點(diǎn)N(b,2), ∴b=﹣3,a=2, ∴a+b=﹣1, ∴(a+b)2014=(﹣1)2014=1. 故答案為:1. 【點(diǎn)評(píng)】本題考查了軸對(duì)稱的性質(zhì)和冪的運(yùn)算,解題的關(guān)鍵是先求得a、b的值. 15.已知點(diǎn)P(3,﹣1)關(guān)于y軸的對(duì)稱點(diǎn)Q的坐標(biāo)是(a+b,1﹣b),則ab的值為 25?。? 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)關(guān)于y軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn):橫坐標(biāo)互為相反數(shù),縱坐標(biāo)不變可直接得到答案. 【解答】解:∵點(diǎn)P(3,﹣1)關(guān)于y軸的對(duì)稱點(diǎn)Q的坐標(biāo)是(a+b,1﹣b), ∴, 解得:, 則ab的值為:(﹣5)2=25. 故答案為:25. 【點(diǎn)評(píng)】此題主要考查了關(guān)于y軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn),關(guān)鍵是掌握點(diǎn)的坐標(biāo)的變化規(guī)律. 16.點(diǎn)A(﹣3,0)關(guān)于y軸的對(duì)稱點(diǎn)的坐標(biāo)是?。?,0)?。? 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)關(guān)于y軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn):橫坐標(biāo)互為相反數(shù),縱坐標(biāo)不變可以直接寫(xiě)出答案. 【解答】解:點(diǎn)A(﹣3,0)關(guān)于y軸的對(duì)稱點(diǎn)的坐標(biāo)是(3,0), 故答案為:(3,0). 【點(diǎn)評(píng)】此題主要考查了關(guān)于y軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn),關(guān)鍵是掌握點(diǎn)的坐標(biāo)的變化規(guī)律. 17.點(diǎn)P(2,﹣1)關(guān)于x軸對(duì)稱的點(diǎn)P′的坐標(biāo)是?。?,1)?。? 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)關(guān)于x軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn):橫坐標(biāo)不變,縱坐標(biāo)互為相反數(shù)可以直接得到答案. 【解答】解:點(diǎn)P(2,﹣1)關(guān)于x軸對(duì)稱的點(diǎn)P′的坐標(biāo)是(2,1), 故答案為:(2,1). 【點(diǎn)評(píng)】此題主要考查了關(guān)于x軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn),關(guān)鍵是掌握點(diǎn)的坐標(biāo)的變化規(guī)律. 18.在平面直角坐標(biāo)系中,點(diǎn)A(2,﹣3)關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)為?。ī?,﹣3)?。? 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)關(guān)于y軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn):橫坐標(biāo)互為相反數(shù),縱坐標(biāo)不變可得答案. 【解答】解:點(diǎn)A(2,﹣3)關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)為(﹣2,﹣3), 故答案為:(﹣2,﹣3). 【點(diǎn)評(píng)】此題主要考查了關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo),關(guān)鍵是掌握點(diǎn)的坐標(biāo)的變化規(guī)律. 19.點(diǎn)P(﹣2,3)關(guān)于x軸的對(duì)稱點(diǎn)P′的坐標(biāo)為?。ī?,﹣3)?。? 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】讓點(diǎn)P的橫坐標(biāo)不變,縱坐標(biāo)互為相反數(shù)即可得到點(diǎn)P關(guān)于x軸的對(duì)稱點(diǎn)P′的坐標(biāo). 【解答】解:∵點(diǎn)P(﹣2,3)關(guān)于x軸的對(duì)稱點(diǎn)P′, ∴點(diǎn)P′的橫坐標(biāo)不變,為﹣2;縱坐標(biāo)為﹣3, ∴點(diǎn)P關(guān)于x軸的對(duì)稱點(diǎn)P′的坐標(biāo)為(﹣2,﹣3). 故答案為:(﹣2,﹣3). 【點(diǎn)評(píng)】此題主要考查了關(guān)于x軸對(duì)稱點(diǎn)的性質(zhì),用到的知識(shí)點(diǎn)為:兩點(diǎn)關(guān)于x軸對(duì)稱,橫縱坐標(biāo)不變,縱坐標(biāo)互為相反數(shù). 20.點(diǎn)P(3,2)關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)是?。ī?,2)?。? 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】此題考查平面直角坐標(biāo)系與對(duì)稱的結(jié)合. 【解答】解:點(diǎn)P(m,n)關(guān)于y軸對(duì)稱點(diǎn)的坐標(biāo)P′(﹣m,n),所以點(diǎn)P(3,2)關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)為(﹣3,2). 故答案為:(﹣3,2). 【點(diǎn)評(píng)】考查平面直角坐標(biāo)系點(diǎn)的對(duì)稱性質(zhì). 21.點(diǎn)P(1,﹣2)關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)為?。ī?,﹣2)?。? 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【專題】常規(guī)題型. 【分析】根據(jù)“關(guān)于y軸對(duì)稱的點(diǎn),縱坐標(biāo)相同,橫坐標(biāo)互為相反數(shù)”解答即可. 【解答】解:點(diǎn)P(1,﹣2)關(guān)于y軸對(duì)稱的點(diǎn)的坐標(biāo)為(﹣1,﹣2). 故答案為:(﹣1,﹣2). 【點(diǎn)評(píng)】本題考查了關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo),解決本題的關(guān)鍵是掌握好對(duì)稱點(diǎn)的坐標(biāo)規(guī)律: (1)關(guān)于x軸對(duì)稱的點(diǎn),橫坐標(biāo)相同,縱坐標(biāo)互為相反數(shù); (2)關(guān)于y軸對(duì)稱的點(diǎn),縱坐標(biāo)相同,橫坐標(biāo)互為相反數(shù); (3)關(guān)于原點(diǎn)對(duì)稱的點(diǎn),橫坐標(biāo)與縱坐標(biāo)都互為相反數(shù). 22.點(diǎn)A(﹣3,2)關(guān)于x軸的對(duì)稱點(diǎn)A′的坐標(biāo)為?。ī?,﹣2)?。? 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)“關(guān)于x軸對(duì)稱的點(diǎn),橫坐標(biāo)相同,縱坐標(biāo)互為相反數(shù)”解答. 【解答】解:點(diǎn)A(﹣3,2)關(guān)于x軸對(duì)稱的點(diǎn)的坐標(biāo)為(﹣3,﹣2). 故答案為:(﹣3,﹣2). 【點(diǎn)評(píng)】本題考查了關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo),解決本題的關(guān)鍵是掌握好對(duì)稱點(diǎn)的坐標(biāo)規(guī)律: (1)關(guān)于x軸對(duì)稱的點(diǎn),橫坐標(biāo)相同,縱坐標(biāo)互為相反數(shù); (2)關(guān)于y軸對(duì)稱的點(diǎn),縱坐標(biāo)相同,橫坐標(biāo)互為相反數(shù); (3)關(guān)于原點(diǎn)對(duì)稱的點(diǎn),橫坐標(biāo)與縱坐標(biāo)都互為相反數(shù). 23.若點(diǎn)A(m+2,3)與點(diǎn)B(﹣4,n+5)關(guān)于y軸對(duì)稱,則m+n= 0?。? 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)“關(guān)于y軸對(duì)稱的點(diǎn),縱坐標(biāo)相同,橫坐標(biāo)互為相反數(shù)”列出方程求解即可. 【解答】解:∵點(diǎn)A(m+2,3)與點(diǎn)B(﹣4,n+5)關(guān)于y軸對(duì)稱, ∴m+2=4,3=n+5, 解得:m=2,n=﹣2, ∴m+n=0, 故答案為:0. 【點(diǎn)評(píng)】本題考查了關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo),解決本題的關(guān)鍵是掌握好對(duì)稱點(diǎn)的坐標(biāo)規(guī)律: (1)關(guān)于x軸對(duì)稱的點(diǎn),橫坐標(biāo)相同,縱坐標(biāo)互為相反數(shù); (2)關(guān)于y軸對(duì)稱的點(diǎn),縱坐標(biāo)相同,橫坐標(biāo)互為相反數(shù); (3)關(guān)于原點(diǎn)對(duì)稱的點(diǎn),橫坐標(biāo)與縱坐標(biāo)都互為相反數(shù). 24.點(diǎn)P(2,3)關(guān)于x軸的對(duì)稱點(diǎn)的坐標(biāo)為?。?,﹣3)?。? 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)關(guān)于x軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn):橫坐標(biāo)不變,縱坐標(biāo)互為相反數(shù).即點(diǎn)P(x,y)關(guān)于x軸的對(duì)稱點(diǎn)P′的坐標(biāo)是(x,﹣y)得出即可. 【解答】解:∵點(diǎn)P(2,3) ∴關(guān)于x軸的對(duì)稱點(diǎn)的坐標(biāo)為:(2,﹣3). 故答案為:(2,﹣3). 【點(diǎn)評(píng)】此題主要考查了關(guān)于x軸、y軸對(duì)稱點(diǎn)的性質(zhì),正確記憶坐標(biāo)規(guī)律是解題關(guān)鍵. 25.已知P(1,﹣2),則點(diǎn)P關(guān)于x軸的對(duì)稱點(diǎn)的坐標(biāo)是?。?,2)?。? 【考點(diǎn)】關(guān)于x軸、y軸對(duì)稱的點(diǎn)的坐標(biāo). 【分析】根據(jù)關(guān)于x軸對(duì)稱點(diǎn)的坐標(biāo)特點(diǎn):橫坐標(biāo)不變,縱坐標(biāo)互為相反數(shù).即點(diǎn)P(x,y)關(guān)于x軸的對(duì)稱點(diǎn)P′的坐標(biāo)是(x,﹣y),進(jìn)而得出答案. 【解答】解:∵P(1,﹣2), ∴點(diǎn)P關(guān)于x軸的對(duì)稱點(diǎn)的坐標(biāo)是:(1,2). 故答案為:(1,2). 【點(diǎn)評(píng)】此題主要考查了關(guān)于x軸對(duì)稱點(diǎn)的性質(zhì),正確記憶關(guān)于坐標(biāo)軸對(duì)稱點(diǎn)的性質(zhì)是解題關(guān)鍵. 三、解答題 26.在如圖所示的直角坐標(biāo)系中,每個(gè)小方格都是邊長(zhǎng)為1的正方形,△ABC的頂點(diǎn)均在格點(diǎn)上,點(diǎn)A的坐標(biāo)是(﹣3,﹣1). (1)將△ABC沿y軸正方向平移3個(gè)單位得到△A1B1C1,畫(huà)出△A1B1C1,并寫(xiě)出點(diǎn)B1坐標(biāo); (2)畫(huà)出△A1B1C1關(guān)于y軸對(duì)稱的△A2B2C2,并寫(xiě)出點(diǎn)C2的坐標(biāo). 【考點(diǎn)】作圖-軸對(duì)稱變換;作圖-平移變換. 【專題】作圖題. 【分析】(1)直接利用平移的性質(zhì)得出平移后對(duì)應(yīng)點(diǎn)位置進(jìn)而得出答案; (2)利用軸對(duì)稱圖形的性質(zhì)得出對(duì)應(yīng)點(diǎn)位置進(jìn)而得出答案. 【解答】解:(1)如圖所示:△A1B1C1,即為所求;點(diǎn)B1坐標(biāo)為:(﹣2,﹣1); (2)如圖所示:△A2B2C2,即為所求,點(diǎn)C2的坐標(biāo)為:(1,1). 【點(diǎn)評(píng)】此題主要考查了軸對(duì)稱變換以及平移變換,根據(jù)圖形的性質(zhì)得出對(duì)應(yīng)點(diǎn)位置是解題關(guān)鍵. 27.如圖,在邊長(zhǎng)為1個(gè)單位長(zhǎng)度的小正方形網(wǎng)格中,給出了△ABC(頂點(diǎn)是網(wǎng)格線的交點(diǎn)). (1)請(qǐng)畫(huà)出△ABC關(guān)于直線l對(duì)稱的△A1B1C1; (2)將線段AC向左平移3個(gè)單位,再向下平移5個(gè)單位,畫(huà)出平移得到的線段A2C2,并以它為一邊作一個(gè)格點(diǎn)△A2B2C2,使A2B2=C2B2. 【考點(diǎn)】作圖-軸對(duì)稱變換;作圖-平移變換. 【分析】(1)利用軸對(duì)稱圖形的性質(zhì)得出對(duì)應(yīng)點(diǎn)位置進(jìn)而得出答案; (2)直接利用平移的性質(zhì)得出平移后對(duì)應(yīng)點(diǎn)位置進(jìn)而得出答案. 【解答】解:(1)如圖所示:△A1B1C1,即為所求; (2)如圖所示:△A2B2C2,即為所求. 【點(diǎn)評(píng)】此題主要考查了軸對(duì)稱變換以及平移變換,根據(jù)圖形的性質(zhì)得出對(duì)應(yīng)點(diǎn)位置是解題關(guān)鍵. 28.在平面直角坐標(biāo)系中,△ABC的頂點(diǎn)坐標(biāo)A(﹣4,1),B(﹣2,1),C(﹣2,3) (1)作△ABC關(guān)于y軸的對(duì)稱圖形△A1B1C1; (2)將△ABC向下平移4個(gè)單位長(zhǎng)度,作出平移后的△A2B2C2; (3)求四邊形AA2B2C的面積. 【考點(diǎn)】作圖-軸對(duì)稱變換;作圖-平移變換. 【分析】(1)分別作出點(diǎn)A、B、C關(guān)于y軸的對(duì)稱的點(diǎn),然后順次連接; (2)分別作出點(diǎn)A、B、C向下平移4個(gè)單位長(zhǎng)度后的點(diǎn),然后順次連接; (3)根據(jù)梯形的面積公式求出四邊形AA2B2C的面積即可. 【解答】解:(1)(2)所作圖形如圖所示: ; (3)四邊形AA2B2C的面積為:(4+6)×2=10. 即四邊形AA2B2C的面積為10. 【點(diǎn)評(píng)】本題考查了根據(jù)平移變換和軸對(duì)稱變換作圖,解答本題的關(guān)鍵是根據(jù)網(wǎng)格結(jié)構(gòu)作出對(duì)應(yīng)點(diǎn),然后順次連接. 29.在平面直角坐標(biāo)系中,已知點(diǎn)A(﹣3,1),B(﹣1,0),C(﹣2,﹣1),請(qǐng)?jiān)趫D中畫(huà)出△ABC,并畫(huà)出與△ABC關(guān)于y軸對(duì)稱的圖形. 【考點(diǎn)】作圖-軸對(duì)稱變換. 【專題】作圖題. 【分析】根據(jù)關(guān)于y軸對(duì)稱點(diǎn)的性質(zhì)得出A,B,C關(guān)于y軸對(duì)稱點(diǎn)的坐標(biāo),進(jìn)而得出答案. 【解答】解:如圖所示:△DEF與△ABC關(guān)于y軸對(duì)稱的圖形. 【點(diǎn)評(píng)】此題主要考查了軸對(duì)稱變換,得出對(duì)應(yīng)點(diǎn)坐標(biāo)是解題關(guān)鍵. 30.如圖,△ABC與△DEF關(guān)于直線l對(duì)稱,請(qǐng)僅用無(wú)刻度的直尺,在下面兩個(gè)圖中分別作出直線l. 【考點(diǎn)】作圖-軸對(duì)稱變換. 【專題】作圖題. 【分析】根據(jù)軸對(duì)稱的性質(zhì),對(duì)應(yīng)邊所在直線的交點(diǎn)一定在對(duì)稱軸上,圖1過(guò)點(diǎn)A和BC與EF的交點(diǎn)作直線即為對(duì)稱軸直線l;圖2,延長(zhǎng)兩組對(duì)應(yīng)邊得到兩個(gè)交點(diǎn),然后過(guò)這兩點(diǎn)作直線即為對(duì)稱軸直線l. 【解答】解:如圖所示. 【點(diǎn)評(píng)】本題考查了利用軸對(duì)稱變換作圖,熟記對(duì)應(yīng)邊所在直線的交點(diǎn)一定在對(duì)稱軸上是解題的關(guān)鍵. 第20頁(yè)(共20頁(yè))- 1.請(qǐng)仔細(xì)閱讀文檔,確保文檔完整性,對(duì)于不預(yù)覽、不比對(duì)內(nèi)容而直接下載帶來(lái)的問(wèn)題本站不予受理。
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