數(shù)學(xué)人教版九年級(jí)上冊(cè)23.2.3　關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo).doc

23.2.3關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo) 1.理解點(diǎn)P與點(diǎn)P關(guān)于原點(diǎn)對(duì)稱時(shí),它們的橫縱坐標(biāo)的關(guān)系,掌握P(x,y)關(guān)于原點(diǎn)對(duì)稱點(diǎn)為P(-x,-y)的運(yùn)用.2.能運(yùn)用關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)關(guān)系特征解決簡(jiǎn)單問題.【重點(diǎn)難點(diǎn)】點(diǎn)P與點(diǎn)P關(guān)于原點(diǎn)對(duì)稱時(shí),它們的橫縱坐標(biāo)的關(guān)系.【新課導(dǎo)入】前面我們知道:兩個(gè)點(diǎn)關(guān)于x軸對(duì)稱,這兩個(gè)點(diǎn)的坐標(biāo)具有一定的規(guī)律;兩個(gè)點(diǎn)關(guān)于y軸對(duì)稱,這兩個(gè)點(diǎn)的坐標(biāo)具有一定的規(guī)律.如果兩個(gè)點(diǎn)關(guān)于原點(diǎn)對(duì)稱時(shí),它們的橫縱坐標(biāo)有什么關(guān)系?【課堂探究】一、關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)特點(diǎn)1.已知點(diǎn)A(x,y-4)與點(diǎn)B(1-y,2x)關(guān)于原點(diǎn)對(duì)稱,則yx的值是(B)(A)1(B)2(C)12(D)-22.(2013安徽節(jié)選)如圖,已知A(-3,-3),B(-2,-1),C(-1,-2)是直角坐標(biāo)平面上三點(diǎn).請(qǐng)畫出ABC關(guān)于原點(diǎn)O對(duì)稱的A1B1C1.解:如圖所示.二、點(diǎn)關(guān)于原點(diǎn)對(duì)稱的應(yīng)用3.直線y=x+3上有一點(diǎn)P(m-5,2m),則P點(diǎn)關(guān)于原點(diǎn)的對(duì)稱點(diǎn)P的坐標(biāo)為(7,4).4.如圖,直線AB與x軸、y軸分別相交于B、A兩點(diǎn),且A(0,3),B(3,0),點(diǎn)A1、點(diǎn)B1是點(diǎn)A、點(diǎn)B關(guān)于原點(diǎn)O的對(duì)稱點(diǎn).(1)在圖中畫出直線A1B1;(2)求出過線段A1B1的函數(shù)解析式.解:(1)如圖所示.(2)y=-x-3.1.關(guān)于原點(diǎn)對(duì)稱的點(diǎn)的坐標(biāo)特征:兩個(gè)點(diǎn)關(guān)于原點(diǎn)對(duì)稱時(shí),它們的坐標(biāo)符號(hào)相反,即點(diǎn)P(x,y)關(guān)于原點(diǎn)的對(duì)稱點(diǎn)為P(-x,-y).2.在坐標(biāo)系內(nèi)作一個(gè)圖形關(guān)于原點(diǎn)對(duì)稱的圖形的“三個(gè)步驟”(1)算:根據(jù)其坐標(biāo)互為相反數(shù),先算出組成圖形的關(guān)鍵點(diǎn)關(guān)于原點(diǎn)的對(duì)稱點(diǎn)的坐標(biāo).(2)描:在坐標(biāo)平面內(nèi)描出對(duì)稱點(diǎn)的位置.(3)連:順次連接各點(diǎn)即為所求作的圖形.1.已知點(diǎn)P(a,3)和P(-4,b)關(guān)于原點(diǎn)對(duì)稱,則(a+b)的值為(A)(A)1(B)-1(C)7(D)-72.若點(diǎn)P(-1-2a,2a-4)關(guān)于原點(diǎn)對(duì)稱的點(diǎn)是第一象限的點(diǎn),則a的整數(shù)解有(B)(A)1個(gè)(B)2個(gè)(C)3個(gè)(D)4個(gè)3.如圖,PQR是ABC經(jīng)過某種變換后得到的圖形.如果ABC中任意一點(diǎn)M的坐標(biāo)為(a,b),那么它的對(duì)應(yīng)點(diǎn)N的坐標(biāo)為(C)(A)(a,-b)(B)(-a,b)(C)(-a,-b)(D)(a,b)4.如圖,在平面直角坐標(biāo)系中,對(duì)ABC進(jìn)行循環(huán)往復(fù)的軸對(duì)稱或中心對(duì)稱變換,若原來點(diǎn)A坐標(biāo)是(a,b),則經(jīng)過第2011次變換后所得的A點(diǎn)坐標(biāo)是(a,-b).5.如圖,畫出ABC關(guān)于原點(diǎn)的對(duì)稱圖形ABC,并求ABC的面積.解:如圖,過C作CDy軸