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23.2.3 關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)
知識(shí)要點(diǎn)基礎(chǔ)練
知識(shí)點(diǎn)1 關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)特征
1.在平面直角坐標(biāo)系中,點(diǎn)P關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)是(C)
A. B.
C. D.
2.已知點(diǎn)P1(-4,3)和P2(-4,-3),則P1和P2(C)
A.關(guān)于原點(diǎn)對(duì)稱
B.關(guān)于y軸對(duì)稱
C.關(guān)于x軸對(duì)稱
D.不存在對(duì)稱關(guān)系
3.△ABC三個(gè)頂點(diǎn)的坐標(biāo)依次為A(1,-1),B(4,1)和C(2,2),將△ABC繞坐標(biāo)原點(diǎn)旋轉(zhuǎn)180°,旋轉(zhuǎn)后所得三角形各頂點(diǎn)的坐標(biāo)依次為 (-1,1) , (-4,-1) , (-2,-2) .?
知識(shí)點(diǎn)2 關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)的應(yīng)用
2、
4.坐標(biāo)平面內(nèi)有兩點(diǎn)P(x,y),Q(m,n),若x+m=0,y+n=0,則點(diǎn)P與點(diǎn)Q(C)
A.關(guān)于x軸對(duì)稱
B.關(guān)于y軸對(duì)稱
C.關(guān)于原點(diǎn)對(duì)稱
D.無對(duì)稱關(guān)系
5.在平面直角坐標(biāo)系中,若點(diǎn)P(m,m-n)與點(diǎn)Q(-4,5)關(guān)于原點(diǎn)對(duì)稱,則點(diǎn)M(m,n)的坐標(biāo)為(B)
A.(2,5) B.(4,9)
C.(3,-2) D.(3,2)
6.若點(diǎn)P(a-5,a+3)關(guān)于原點(diǎn)對(duì)稱的點(diǎn)在第四象限,則a的取值范圍為 -3
3、的橫坐標(biāo)都乘以-1,縱坐標(biāo)都乘以-1,符合上述要求的圖是(C)
9.若點(diǎn)P(-a,a-3)關(guān)于原點(diǎn)對(duì)稱的點(diǎn)是第二象限內(nèi)的點(diǎn),則a滿足(C)
A.a>3 B.03
10.在平面直角坐標(biāo)系中,若點(diǎn)P(x,y)在第二象限,且|x|-1=0,y2-4=0,則點(diǎn)P關(guān)于坐標(biāo)原點(diǎn)對(duì)稱的點(diǎn)P'的坐標(biāo)是(B)
A.P'(-1,-2) B.P'(1,-2)
C.P'(-1,2) D.P'(1,2)
11.若點(diǎn)A(-3,n)在x軸上,則點(diǎn)B(n-1,n+1)關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)為 (1,-1) .?
12.若點(diǎn)A(3-m,2)在函數(shù)y=2x-4的圖象上,則
4、點(diǎn)A關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)是 (-3,-2) .?
13.在平面直角坐標(biāo)系中,點(diǎn)P關(guān)于原點(diǎn)的對(duì)稱點(diǎn)為P1,點(diǎn)P關(guān)于x軸的對(duì)稱點(diǎn)為P2(a,b),則= -2 .?
14.如圖,已知A(2,3)和直線y=x.
(1)分別寫出點(diǎn)A關(guān)于直線y=x的對(duì)稱點(diǎn)B和關(guān)于原點(diǎn)的對(duì)稱點(diǎn)C的坐標(biāo).
(2)若點(diǎn)D是點(diǎn)B關(guān)于原點(diǎn)的對(duì)稱點(diǎn),判斷四邊形ABCD的形狀,并說明理由.
解:(1)點(diǎn)A關(guān)于直線y=x的對(duì)稱點(diǎn)B和關(guān)于原點(diǎn)的對(duì)稱點(diǎn)C的坐標(biāo)分別為B(3,2),C(-2,-3).
(2)四邊形ABCD是矩形.理由如下:∵B(3,2)關(guān)于原點(diǎn)的對(duì)稱點(diǎn)為D(-3,-2),又∵點(diǎn)B和點(diǎn)D關(guān)于原點(diǎn)對(duì)稱,∴BO=D
5、O.同理AO=DO,∴四邊形ABCD是平行四邊形.∵A關(guān)于直線y=x的對(duì)稱點(diǎn)為B,點(diǎn)A關(guān)于原點(diǎn)的對(duì)稱點(diǎn)C,∴AC=BD,∴四邊形ABCD是矩形.
15.已知點(diǎn)A(3a-3,-5a-2)關(guān)于原點(diǎn)的對(duì)稱點(diǎn)為B,而點(diǎn)B關(guān)于y軸的對(duì)稱點(diǎn)C在第二象限,化簡(jiǎn).
解:∵A(3a-3,-5a-2)關(guān)于原點(diǎn)的對(duì)稱點(diǎn)為B,∴B的坐標(biāo)為(3-3a,5a+2).又∵點(diǎn)B和點(diǎn)C關(guān)于y軸對(duì)稱,∴C點(diǎn)坐標(biāo)為(3a-3,5a+2).∵C點(diǎn)在第二象限,∴3a-3<0,3(a-1)<0,a<1;5a+2>0,a>-,∴原式==5a+2-(1-a)=6a+1.
16.在平面直角坐標(biāo)系xOy中,已知A(-1,5),B(4,2)
6、,C(-1,0)三點(diǎn).
(1)求點(diǎn)A關(guān)于原點(diǎn)O的對(duì)稱點(diǎn)A'的坐標(biāo),點(diǎn)B關(guān)于x軸的對(duì)稱點(diǎn)B'的坐標(biāo),點(diǎn)C關(guān)于y軸的對(duì)稱點(diǎn)C'的坐標(biāo);
(2)求(1)中的△A'B'C'的面積.
解:(1)A',B',C'三點(diǎn)坐標(biāo)分別為A'(1,-5),B'(4,-2),C'(1,0)
(2)如圖所示.S△A'B'C'=×5×3=.
拓展探究突破練
17.如圖所示,在平面直角坐標(biāo)系中,點(diǎn)P(1,0)作如下實(shí)驗(yàn):先向上平移(后一次平移比前一次多1個(gè)單位長(zhǎng)度),再作關(guān)于原點(diǎn)的對(duì)稱點(diǎn),即向上平移1個(gè)單位得到點(diǎn)P1,作點(diǎn)P1關(guān)于原點(diǎn)的對(duì)稱點(diǎn)P2,再向上平移2個(gè)單位得到P3,作P3關(guān)于原點(diǎn)的對(duì)稱點(diǎn)P4,…,那么點(diǎn)P2015的坐標(biāo)是 (-1,504) .?
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2018年秋九年級(jí)數(shù)學(xué)上冊(cè) 第二十三章《旋轉(zhuǎn)》23.2 中心對(duì)稱 23.2.3 關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)試題 （新版）新人教版
