八年級(jí)數(shù)學(xué)用坐標(biāo)表示軸對(duì)稱試卷及答案

一、單項(xiàng)選擇題（每題2分，共20分）1.點(diǎn)\(A(3,-2)\)關(guān)于\(x\)軸對(duì)稱的點(diǎn)的坐標(biāo)是（）A.\((3,2)\)B.\((-3,-2)\)C.\((-3,2)\)D.\((2,-3)\)2.點(diǎn)\(P(-5,6)\)關(guān)于\(y\)軸對(duì)稱的點(diǎn)的坐標(biāo)是（）A.\((5,-6)\)B.\((-5,-6)\)C.\((5,6)\)D.\((6,-5)\)3.已知點(diǎn)\(A\)的坐標(biāo)為\((a,b)\)，則點(diǎn)\(A\)關(guān)于直線\(x=2\)對(duì)稱的點(diǎn)的橫坐標(biāo)為（）A.\(4-a\)B.\(a-4\)C.\(2-a\)D.\(a-2\)4.若點(diǎn)\(M(1-2m,m-1)\)關(guān)于\(x\)軸對(duì)稱的點(diǎn)在第一象限，則\(m\)的取值范圍是（）A.\(m\gt\frac{1}{2}\)B.\(m\lt1\)C.\(\frac{1}{2}\ltm\lt1\)D.\(m\lt\frac{1}{2}\)5.點(diǎn)\(A(-2,3)\)關(guān)于直線\(y=1\)對(duì)稱的點(diǎn)的坐標(biāo)是（）A.\((-2,-1)\)B.\((-2,-3)\)C.\((2,1)\)D.\((-2,1)\)6.點(diǎn)\((3,-4)\)關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)是（）A.\((-3,4)\)B.\((3,4)\)C.\((-3,-4)\)D.\((4,-3)\)7.已知點(diǎn)\(A(x,4)\)與點(diǎn)\(B(3,y)\)關(guān)于\(y\)軸對(duì)稱，那么\(x+y\)的值為（）A.-1B.1C.7D.-78.在平面直角坐標(biāo)系中，點(diǎn)\(A(-3,4)\)關(guān)于直線\(x=-1\)對(duì)稱的點(diǎn)\(A'\)的坐標(biāo)是（）A.\((-1,4)\)B.\((1,4)\)C.\((-3,2)\)D.\((-3,0)\)9.若點(diǎn)\(P(a,2)\)與點(diǎn)\(Q(-1,b)\)關(guān)于\(y\)軸對(duì)稱，則\(a+b\)的值為（）A.-1B.1C.3D.-310.點(diǎn)\(M(-2,5)\)關(guān)于直線\(y=-2\)對(duì)稱的點(diǎn)的坐標(biāo)是（）A.\((-2,-9)\)B.\((-2,-7)\)C.\((-2,-1)\)D.\((-2,-5)\)二、多項(xiàng)選擇題（每題2分，共20分）1.下列說法正確的是（）A.點(diǎn)\((-3,2)\)關(guān)于\(x\)軸對(duì)稱的點(diǎn)是\((-3,-2)\)B.點(diǎn)\((2,-4)\)關(guān)于\(y\)軸對(duì)稱的點(diǎn)是\((-2,-4)\)C.點(diǎn)\((-1,0)\)關(guān)于原點(diǎn)對(duì)稱的點(diǎn)是\((1,0)\)D.點(diǎn)\((5,-3)\)關(guān)于直線\(x=3\)對(duì)稱的點(diǎn)是\((1,-3)\)2.點(diǎn)\(A(2,-3)\)，關(guān)于\(x\)軸、\(y\)軸、原點(diǎn)對(duì)稱的點(diǎn)分別為\(A_1\)、\(A_2\)、\(A_3\)，則下列說法正確的是（）A.\(A_1\)的坐標(biāo)為\((2,3)\)B.\(A_2\)的坐標(biāo)為\((-2,-3)\)C.\(A_3\)的坐標(biāo)為\((-2,3)\)D.\(A_1\)、\(A_2\)、\(A_3\)三點(diǎn)在同一條直線上3.平面直角坐標(biāo)系中，與點(diǎn)\(M(-2,3)\)關(guān)于某條直線對(duì)稱的點(diǎn)是\(N(2,3)\)，則這條直線可以是（）A.\(x=0\)B.\(y=0\)C.\(x=1\)D.\(y=3\)4.若點(diǎn)\(P(x,y)\)關(guān)于\(x\)軸對(duì)稱的點(diǎn)\(P_1\)的坐標(biāo)為\((m,n)\)，關(guān)于\(y\)軸對(duì)稱的點(diǎn)\(P_2\)的坐標(biāo)為\((a,b)\)，則（）A.\(m=x\)B.\(n=-y\)C.\(a=-x\)D.\(b=y\)5.點(diǎn)\(A(-3,4)\)關(guān)于直線\(y=x\)對(duì)稱的點(diǎn)\(A'\)，關(guān)于直線\(y=-x\)對(duì)稱的點(diǎn)\(A''\)，則（）A.\(A'\)的坐標(biāo)為\((4,-3)\)B.\(A''\)的坐標(biāo)為\((-4,3)\)C.\(A\)、\(A'\)、\(A''\)三點(diǎn)構(gòu)成直角三角形D.\(A\)、\(A'\)、\(A''\)三點(diǎn)構(gòu)成等腰三角形6.以下點(diǎn)的坐標(biāo)變化中，是關(guān)于\(y\)軸對(duì)稱的有（）A.\((1,2)\)變?yōu)閈((-1,2)\)B.\((-3,-4)\)變?yōu)閈((3,-4)\)C.\((5,0)\)變?yōu)閈((-5,0)\)D.\((0,-6)\)變?yōu)閈((0,6)\)7.已知點(diǎn)\(A(a,b)\)，點(diǎn)\(B(c,d)\)，若點(diǎn)\(A\)與點(diǎn)\(B\)關(guān)于\(x\)軸對(duì)稱，則（）A.\(a=c\)B.\(b=-d\)C.\(a=-c\)D.\(b=d\)8.點(diǎn)\(P(x,y)\)在第二象限，且關(guān)于\(x\)軸對(duì)稱的點(diǎn)\(P_1\)到\(x\)軸的距離是\(3\)，關(guān)于\(y\)軸對(duì)稱的點(diǎn)\(P_2\)到\(y\)軸的距離是\(4\)，則（）A.\(x=-4\)B.\(y=3\)C.\(P\)的坐標(biāo)為\((-4,3)\)D.\(P_1\)的坐標(biāo)為\((-4,-3)\)9.平面直角坐標(biāo)系中，點(diǎn)\(M(1,-2)\)關(guān)于直線\(x=-2\)對(duì)稱的點(diǎn)\(M_1\)，關(guān)于直線\(y=1\)對(duì)稱的點(diǎn)\(M_2\)，則（）A.\(M_1\)的坐標(biāo)為\((-5,-2)\)B.\(M_2\)的坐標(biāo)為\((1,4)\)C.\(M\)、\(M_1\)、\(M_2\)三點(diǎn)構(gòu)成三角形D.\(M_1M_2\)的長(zhǎng)度為\(9\)10.若點(diǎn)\(A(x_1,y_1)\)與點(diǎn)\(B(x_2,y_2)\)關(guān)于直線\(x=m\)對(duì)稱，則（）A.\(x_1+x_2=2m\)B.\(y_1=y_2\)C.\(x_1-x_2=2m\)D.\(y_1+y_2=2m\)三、判斷題（每題2分，共20分）1.點(diǎn)\((-5,6)\)關(guān)于\(y\)軸對(duì)稱的點(diǎn)的坐標(biāo)是\((5,6)\)。（）2.點(diǎn)\(A(3,-4)\)關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)是\((-3,4)\)。（）3.點(diǎn)\((2,5)\)關(guān)于直線\(x=3\)對(duì)稱的點(diǎn)是\((4,5)\)。（）4.若點(diǎn)\(P(a,b)\)關(guān)于\(x\)軸對(duì)稱的點(diǎn)是\(P_1\)，則\(P_1\)的坐標(biāo)為\((-a,b)\)。（）5.點(diǎn)\((-1,-2)\)關(guān)于直線\(y=-1\)對(duì)稱的點(diǎn)是\((-1,0)\)。（）6.關(guān)于\(y\)軸對(duì)稱的兩個(gè)點(diǎn)的縱坐標(biāo)相等，橫坐標(biāo)互為相反數(shù)。（）7.點(diǎn)\((0,3)\)關(guān)于原點(diǎn)對(duì)稱的點(diǎn)是\((0,-3)\)。（）8.點(diǎn)\(A(-4,2)\)關(guān)于直線\(y=x\)對(duì)稱的點(diǎn)的坐標(biāo)是\((2,-4)\)。（）9.若點(diǎn)\(M(1,-3)\)與點(diǎn)\(N\)關(guān)于直線\(y=-2\)對(duì)稱，則點(diǎn)\(N\)的坐標(biāo)是\((1,-1)\)。（）10.關(guān)于\(x\)軸對(duì)稱的兩個(gè)點(diǎn)的橫坐標(biāo)相等，縱坐標(biāo)互為相反數(shù)。（）四、簡(jiǎn)答題（每題5分，共20分）1.已知點(diǎn)\(A(-2,4)\)，求點(diǎn)\(A\)關(guān)于\(x\)軸、\(y\)軸、原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)。-答案：關(guān)于\(x\)軸對(duì)稱的點(diǎn)坐標(biāo)是\((-2,-4)\)；關(guān)于\(y\)軸對(duì)稱的點(diǎn)坐標(biāo)是\((2,4)\)；關(guān)于原點(diǎn)對(duì)稱的點(diǎn)坐標(biāo)是\((2,-4)\)。2.點(diǎn)\(P(3a-1,2+a)\)在第二象限的角平分線上，求\(a\)的值及點(diǎn)\(P\)關(guān)于\(x\)軸對(duì)稱的點(diǎn)的坐標(biāo)。-答案：第二象限角平分線上點(diǎn)的橫縱坐標(biāo)互為相反數(shù)，即\(3a-1+2+a=0\)，解得\(a=-\frac{1}{4}\)。\(P\)點(diǎn)坐標(biāo)為\((-\frac{7}{4},\frac{7}{4})\)，關(guān)于\(x\)軸對(duì)稱點(diǎn)坐標(biāo)是\((-\frac{7}{4},-\frac{7}{4})\)。3.平面直角坐標(biāo)系中，點(diǎn)\(A(1,3)\)關(guān)于直線\(x=4\)對(duì)稱的點(diǎn)\(A'\)的坐標(biāo)是多少？-答案：點(diǎn)\(A(1,3)\)與對(duì)稱點(diǎn)\(A'\)的縱坐標(biāo)不變，橫坐標(biāo)到直線\(x=4\)的距離相等。\(4-1=3\)，所以\(A'\)橫坐標(biāo)為\(4+3=7\)，\(A'\)坐標(biāo)為\((7,3)\)。4.已知點(diǎn)\(M(x,y)\)，若點(diǎn)\(M\)關(guān)于直線\(y=-1\)對(duì)稱的點(diǎn)為\(N\)，寫出點(diǎn)\(N\)的坐標(biāo)表達(dá)式。-答案：點(diǎn)\(M(x,y)\)與點(diǎn)\(N\)的橫坐標(biāo)相同，縱坐標(biāo)到直線\(y=-1\)距離相等。所以\(N\)的縱坐標(biāo)為\(-1-(y+1)=-2-y\)，\(N\)坐標(biāo)為\((x,-2-y)\)。五、討論題（每題5分，共20分）1.在平面直角坐標(biāo)系中，一個(gè)點(diǎn)關(guān)于\(x\)軸、\(y\)軸、原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)變化規(guī)律在實(shí)際解題中有哪些應(yīng)用？請(qǐng)舉例說明。-答案：在求圖形關(guān)于坐標(biāo)軸或原點(diǎn)對(duì)稱的圖形坐標(biāo)時(shí)常用。比如求三角形\(ABC\)關(guān)于\(y\)軸對(duì)稱的三角形\(A'B'C'\)坐標(biāo)，利用\(y\)軸對(duì)稱點(diǎn)縱坐標(biāo)不變，橫坐標(biāo)互為相反數(shù)，可快速得出\(A'\)、\(B'\)、\(C'\)坐標(biāo)。2.當(dāng)點(diǎn)\(P(x,y)\)在不同象限移動(dòng)時(shí)，它關(guān)于直線\(x=a\)（\(a\)為常數(shù)）對(duì)稱的點(diǎn)\(P'\)的坐標(biāo)變化有什么特點(diǎn)？請(qǐng)討論。-答案：若\(P(x,y)\)在不同象限，\(P\)與\(P'\)縱坐標(biāo)不變。\(P\)與直線\(x=a\)距離為\(\vertx-a\vert\)，則\(P'\)橫坐標(biāo)為\(2a-x\)。如\(P\)在第一象限，\(x\gta\)時(shí)，\(P'\)橫坐標(biāo)小于\(a\)。3.討論點(diǎn)\(A(x_1,y_1)\)關(guān)于直線\(y=x+b\)對(duì)稱的點(diǎn)\(A'\)的坐標(biāo)求法思路。-答案：先設(shè)\(A'(x_2,y_2)\)，直線\(AA'\)與直線\(y=x+b\)垂直，斜率乘積為\(-1\)，可得一個(gè)方程；\(AA'\)中點(diǎn)\((\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)在直線\(y=x+b\)上，又得一個(gè)方程，聯(lián)立求解可得\(A'\)坐標(biāo)。4.平面直角坐標(biāo)系中，關(guān)于直線\(y=-x+c\)對(duì)稱的兩點(diǎn)坐標(biāo)之間有怎樣的關(guān)系？請(qǐng)?zhí)接憽?答案：設(shè)兩點(diǎn)\(M(x_1,y_1)\)，\(N(x_2,y_2)\)關(guān)于直線\(y=-x+c\)對(duì)稱。直線\(MN\)與已知直線垂直，斜率為\(1\)，得\(\frac{y_2-y_1}{x_2-x_1}=1\)；\(MN\)中點(diǎn)\((\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})\)在直線\(y=-x+c\)上，即\(\frac{y_1+y_2}{2}=-