課時(shí)3關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)1.[2021賀州中考]在平面直角坐標(biāo)系中,點(diǎn)A(3,2)關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)是(

)A.(-3,2) B.(3,-2)C.(-2,-3) D.(-3,-2)知識(shí)點(diǎn)1關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)答案1.D2.[2022咸寧模擬]在平面直角坐標(biāo)系中,將點(diǎn)P(-1,-2)向右平移3個(gè)單位長(zhǎng)度得到點(diǎn)P1,則點(diǎn)P1關(guān)于原點(diǎn)對(duì)稱的點(diǎn)P2的坐標(biāo)為(

)A.(2,-2) B.(-2,2)C.(-2,-2) D.(-3,2)知識(shí)點(diǎn)1關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)答案2.B

因?yàn)閷Ⅻc(diǎn)P(-1,-2)向右平移3個(gè)單位長(zhǎng)度得到點(diǎn)P1,所以點(diǎn)P1的坐標(biāo)為(2,-2),所以點(diǎn)P1關(guān)于原點(diǎn)對(duì)稱的點(diǎn)P2的坐標(biāo)為(-2,2).3.

在平面直角坐標(biāo)系中,將△AOB

繞原點(diǎn)O

順時(shí)針旋轉(zhuǎn)180°后得到△A1OB1,若點(diǎn)B的坐標(biāo)為(2,1),則點(diǎn)B的對(duì)應(yīng)點(diǎn)B1的坐標(biāo)為(

)A.(1,2) B.(2,-1)C.(-2,1) D.(-2,-1)知識(shí)點(diǎn)1關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)答案3.D

由題意可知△A1OB1與△AOB關(guān)于原點(diǎn)O成中心對(duì)稱,∵點(diǎn)B的坐標(biāo)為(2,1),∴點(diǎn)B1的坐標(biāo)為(-2,-1).4.[2022信陽(yáng)模擬]若點(diǎn)P(a+1,a-2)關(guān)于原點(diǎn)對(duì)稱的點(diǎn)位于第二象限,則a的取值范圍在數(shù)軸上表示正確的是(

)知識(shí)點(diǎn)1關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)答案4.C

∵點(diǎn)P(a+1,a-2)關(guān)于原點(diǎn)對(duì)稱的點(diǎn)在第二象限,∴點(diǎn)P在第四象限,∴a+1>0,a-2<0,∴-1<a<2,結(jié)合選項(xiàng),知C項(xiàng)正確.5.[2022西安月考]已知點(diǎn)P(x,y)在第二象限,|x|=6,|y|=8,則點(diǎn)P關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)為

.

知識(shí)點(diǎn)1關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)答案5.(6,-8)

因?yàn)閨x|=6,|y|=8,所以x=±6,y=±8.因?yàn)辄c(diǎn)P(x,y)在第二象限,所以x=-6,y=8,所以點(diǎn)P的坐標(biāo)為(-6,8),所以點(diǎn)P關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)為(6,-8).6.

教材P70習(xí)題23.2T4變式[2022三門峽期中]已知P1(a,-2)和P2(3,b)關(guān)于原點(diǎn)對(duì)稱,則(a+b)2022的值為

.

知識(shí)點(diǎn)1關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)答案6.1

因?yàn)镻1(a,-2)和P2(3,b)關(guān)于原點(diǎn)對(duì)稱,所以a=-3,b=2,所以(a+b)2022=(-3+2)2022=1.7.[2022成都嘉祥外國(guó)語(yǔ)學(xué)校期中]若點(diǎn)A(-2,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

.

知識(shí)點(diǎn)1關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)答案7.(1,-1)

因?yàn)辄c(diǎn)A(-2,n)在x軸上,所以n=0,所以點(diǎn)B的坐標(biāo)為(-1,1),所以點(diǎn)B關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)為(1,-1).8.

已知點(diǎn)P(x2+2x,3)在第二象限,且與點(diǎn)Q(x+2,y)關(guān)于原點(diǎn)對(duì)稱,試求x+2y的值.知識(shí)點(diǎn)1關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)答案8.解:根據(jù)題意,得(x2+2x)+(x+2)=0,y=-3.解方程(x2+2x)+(x+2)=0,得x1=-1,x2=-2.當(dāng)x=-1時(shí),x2+2x=-1,點(diǎn)P(-1,3)在第二象限,符合題意.當(dāng)x=-2時(shí),x2+2x=0,與點(diǎn)P在第二象限矛盾,不符合題意,舍去.∴x=-1,y=-3,∴x+2y=-7.9.

如圖,在平面直角坐標(biāo)系中,△ABC的三個(gè)頂點(diǎn)坐標(biāo)分別為A(-2,1),B(-1,3),C(-2,4).(1)畫出△ABC關(guān)于原點(diǎn)O對(duì)稱的△A1B1C1,并寫出點(diǎn)B1的坐標(biāo);(2)畫出△ABC繞原點(diǎn)O順時(shí)針旋轉(zhuǎn)90°得到的△A2B2C2,并寫出點(diǎn)A2的坐標(biāo).知識(shí)點(diǎn)2作已知圖形關(guān)于原點(diǎn)對(duì)稱的圖形答案9.解:(1)△A1B1C1如圖所示,點(diǎn)B1的坐標(biāo)為(1,-3).(2)△A2B2C2如圖所示,點(diǎn)A2的坐標(biāo)為(1,2).

答案

2.[2021邯鄲二十三中期中]“小馬虎”在做作業(yè)時(shí),將點(diǎn)A橫縱坐標(biāo)的順序顛倒了,誤寫為A(-b,a),“小糊涂”也不細(xì)心,將點(diǎn)B的坐標(biāo)寫成其關(guān)于x軸對(duì)稱的點(diǎn)的坐標(biāo),誤寫為B(-a,-b),則A,B兩點(diǎn)原來(lái)的位置關(guān)系是(

)A.關(guān)于x軸對(duì)稱 B.關(guān)于原點(diǎn)對(duì)稱C.關(guān)于y軸對(duì)稱 D.A和B重合答案2.B

由題意,得點(diǎn)A的坐標(biāo)為(a,-b),點(diǎn)B的坐標(biāo)為(-a,b),所以點(diǎn)A與點(diǎn)B關(guān)于原點(diǎn)對(duì)稱.3.

已知點(diǎn)P(-1,m2+1)與點(diǎn)Q關(guān)于原點(diǎn)對(duì)稱,則點(diǎn)Q一定在(

)A.第一象限 B.第二象限C.第三象限 D.第四象限答案3.D

∵點(diǎn)P(-1,m2+1)與點(diǎn)Q關(guān)于原點(diǎn)對(duì)稱,∴Q(1,-m2-1).∵-m2-1≤-1,∴點(diǎn)Q一定在第四象限.4.[2022邯鄲期末]若點(diǎn)A(a,b)和點(diǎn)B(m,n)關(guān)于原點(diǎn)對(duì)稱,且a+b=1,則m+n的值為

.

答案4.-1

∵點(diǎn)A(a,b)和點(diǎn)B(m,n)關(guān)于原點(diǎn)對(duì)稱,∴m=-a,n=-b.∵a+b=1,∴m+n=-a-b=-(a+b)=-1.5.

在平面直角坐標(biāo)系中,已知A(2,3),B(0,1),C(3,1),若線段AC與BD互相平分,則點(diǎn)D關(guān)于坐標(biāo)原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)為

.

答案5.(-5,-3)

根據(jù)題意,畫出圖形如圖所示,∵線段AC與BD互相平分,∴點(diǎn)D的坐標(biāo)為(5,3),∴點(diǎn)D關(guān)于坐標(biāo)原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)為(-5,-3).6.[2022濮陽(yáng)期中]在平面直角坐標(biāo)系中,已知A(3,2),作點(diǎn)A關(guān)于y軸的對(duì)稱點(diǎn)A1,點(diǎn)A1關(guān)于原點(diǎn)的對(duì)稱點(diǎn)A2,點(diǎn)A2關(guān)于x軸的對(duì)稱點(diǎn)A3,點(diǎn)A3關(guān)于y軸的對(duì)稱點(diǎn)A4……按此規(guī)律,則點(diǎn)A2021的坐標(biāo)為

.

答案6.(3,-2)

根據(jù)題意,得點(diǎn)A1的坐標(biāo)為(-3,2),點(diǎn)A2的坐標(biāo)為(3,-2),點(diǎn)A3的坐標(biāo)為(3,2),點(diǎn)A4的坐標(biāo)為(-3,2)……由此可知每3次變換為一循環(huán).因?yàn)?021÷3=673……2,所以點(diǎn)A2021的坐標(biāo)為(3,-2).7.[2022南昌期中]在邊長(zhǎng)為1個(gè)單位長(zhǎng)度的正方形網(wǎng)格中建立如圖所示的平面直角坐標(biāo)系,△ABC的頂點(diǎn)都在格點(diǎn)上,請(qǐng)解答下列問題:(1)作出△ABC向左平移4個(gè)單位長(zhǎng)度后得到的△A1B1C1,并寫出點(diǎn)C1的坐標(biāo);(2)作出△ABC關(guān)于原點(diǎn)O對(duì)稱的△A2B2C2,并寫出點(diǎn)C2的坐標(biāo);(3)已知△ABC關(guān)于直線l對(duì)