人教版(2023)八年級(jí)上冊(cè)數(shù)學(xué)同步練習(xí)：13.2 第2課時(shí)　用坐標(biāo)表示軸對(duì)稱(chēng)(含答案)【可編輯可打印】

人教版(2023版)初中數(shù)學(xué)八年級(jí)上冊(cè)第2課時(shí)用坐標(biāo)表示軸對(duì)稱(chēng)知能演練提升一、能力提升1.若點(diǎn)P關(guān)于x軸對(duì)稱(chēng)的點(diǎn)是它本身,則點(diǎn)P()A.在x軸上 B.在y軸上C.是原點(diǎn) D.是任意一點(diǎn)2.已知點(diǎn)A(a,2)與點(diǎn)B(3,b)關(guān)于x軸對(duì)稱(chēng),則實(shí)數(shù)a,b的值是()A.a=3,b=2 B.a=-3,b=2C.a=3,b=-2 D.a=-3,b=-23.已知點(diǎn)P(-1-2a,5)關(guān)于x軸的對(duì)稱(chēng)點(diǎn)和點(diǎn)M(3,b)關(guān)于y軸的對(duì)稱(chēng)點(diǎn)相同,則點(diǎn)A(a,b)關(guān)于x軸對(duì)稱(chēng)的點(diǎn)的坐標(biāo)為()A.(1,-5) B.(1,5)C.(-1,5) D.(-1,-5)4.如圖,陰影部分組成的圖案既是關(guān)于x軸成軸對(duì)稱(chēng)的圖形,又是關(guān)于y軸成軸對(duì)稱(chēng)的圖形.若點(diǎn)A的坐標(biāo)是(1,3),則點(diǎn)M和點(diǎn)N的坐標(biāo)分別為()A.M(1,-3),N(-1,-3) B.M(-1,-3),N(-1,3)C.M(-1,-3),N(1,-3) D.M(-1,3),N(1,-3)5.在平面直角坐標(biāo)系中,規(guī)定把一個(gè)三角形先沿著x軸翻折,再向右平移2個(gè)單位稱(chēng)為1次變換.如圖,已知等邊三角形ABC的頂點(diǎn)B的坐標(biāo)是(-1,-1),把△ABC經(jīng)過(guò)連續(xù)3次這樣的變換得到△A'B'C',則點(diǎn)B的對(duì)應(yīng)點(diǎn)B'的坐標(biāo)是.

6.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(chēng)點(diǎn),得到點(diǎn)A',再作點(diǎn)A'關(guān)于y軸的對(duì)稱(chēng)點(diǎn),得到點(diǎn)A″,則點(diǎn)A″的坐標(biāo)是.

7.如圖,已知在△ABC中,BC∥x軸,BC=2,點(diǎn)A的坐標(biāo)是(-4,3),點(diǎn)B的坐標(biāo)是(-3,1).(1)畫(huà)出△ABC關(guān)于y軸對(duì)稱(chēng)的△A'B'C',并指出A',B',C'的坐標(biāo);(2)求以點(diǎn)A,B,A',B'為頂點(diǎn)的四邊形的面積.二、創(chuàng)新應(yīng)用8.根據(jù)指令[m,h,y=b](或[m,h,x=a]),機(jī)器人在平面直角坐標(biāo)系中能完成下列動(dòng)作:先由原點(diǎn)向左(m<0)或向右(m>0)平移|m|個(gè)長(zhǎng)度單位到達(dá)點(diǎn)A,再由點(diǎn)A向上(h>0)或向下(h<0)平移|h|個(gè)長(zhǎng)度單位到達(dá)點(diǎn)B,再跳到點(diǎn)B關(guān)于直線(xiàn)y=b(或x=a)的對(duì)稱(chēng)點(diǎn)C處.(1)若給機(jī)器人下了一個(gè)指令[4,0,y=-3],則點(diǎn)C的坐標(biāo)為;

(2)若給機(jī)器人下了一個(gè)指令[-3,2,x=4],則點(diǎn)C的坐標(biāo)為;

(3)請(qǐng)你給機(jī)器人下一個(gè)指令,使其移動(dòng)到點(diǎn)(-5,10)處.

知能演練·提升一、能力提升1.A關(guān)于x軸對(duì)稱(chēng)的點(diǎn)的坐標(biāo)特征是橫坐標(biāo)不變,縱坐標(biāo)變成它的相反數(shù).而點(diǎn)P關(guān)于x軸對(duì)稱(chēng)的點(diǎn)是它本身,所以點(diǎn)P的縱坐標(biāo)只能為0,即點(diǎn)P在x軸上.2.C3.B4.C由題意知,點(diǎn)N與點(diǎn)A關(guān)于x軸成軸對(duì)稱(chēng),點(diǎn)M與點(diǎn)N關(guān)于y軸成軸對(duì)稱(chēng).因?yàn)辄c(diǎn)A的坐標(biāo)是(1,3),所以點(diǎn)N的坐標(biāo)是(1,-3),所以點(diǎn)M的坐標(biāo)是(-1,-3).5.(5,1)6.(-2,3)點(diǎn)A(2,-3)關(guān)于x軸的對(duì)稱(chēng)點(diǎn)A'的坐標(biāo)為(2,3).點(diǎn)A'關(guān)于y軸的對(duì)稱(chēng)點(diǎn)A″的坐標(biāo)是(-2,3).7.分析根據(jù)題意,點(diǎn)C的坐標(biāo)為(-1,1),所以點(diǎn)A'(4,3),B'(3,1),C'(1,1).四邊形ABB'A'是梯形,上底AA'=8,下底BB'=6,高為2.解(1)如圖,點(diǎn)A'(4,3),B'(3,1),C'(1,1).(2)連接AA',CC',如上圖.由(1)知,AA'=8,BB'=6,高為2,故四邊形ABB'A'的面積S=8+62×2=14二、創(chuàng)新應(yīng)用8.(