三角形A(4,1),B(7,5),C(-4,7)，求角A平分线方程

[[{"txt": "\u5728\u25b3ABC\u4e2d,A(4,1),B(7,5),C(-4,7),\u7528\u4e09\u79cd\u65b9\u6cd5\u6c42\u2220A\u7684\u5e73\u5206\u7ebf\u7684\u65b9\u7a0b\u3002"}, {"img": ["https://exp-picture.cdn.bcebos.com/ab966c6b0ce265e742c60dcb9f23beb9773eb71c.m2m?x-bce-process=image%2Fresize%2Cm_lfit%2Cw_500%2Climit_1"]}], [{"txt": ["\u5de5\u5177/\u539f\u6599"]}, {"txt": "\u77e5\u8bc6\u70b9\u4e00\uff1a\u89d2\u5e73\u5206\u7ebf\u5b9a\u7406\u53ca\u4e24\u70b9\u8ddd\u79bb\u516c\u5f0f"}, {"txt": "\u77e5\u8bc6\u70b9\u4e8c\uff1a\u5230\u89d2\u77e5\u8bc6\u5e94\u7528"}, {"txt": "\u77e5\u8bc6\u70b9\u4e09\uff1a\u5411\u91cf\u77e5\u8bc6\u7684\u5e94\u7528"}], [{"txt": ["\u65b9\u6cd5/\u6b65\u9aa41\uff1a\u89d2\u5e73\u5206\u7ebf\u5b9a\u7406\u53ca\u4e24\u70b9\u8ddd\u79bb\u516c\u5f0f"]}, {"txt": "\u00a0\u00a0[\u89e3\u9898\u601d\u8def]\uff1a\u56e0\u4e3a\u662f\u89d2\u5e73\u5206\u7ebf\uff0c\u5229\u7528\u89d2\u5e73\u7ebf\u5b9a\u7406\u5373\u4e24\u70b9\u95f4\u8ddd\u79bb\u516c\u5f0f\u6765\u6c42\u70b9D\uff0c\u8fdb\u800c\u6c42\u5176\u65b9\u7a0b\u3002"}, {"txt": "\u6839\u636e\u4e24\u70b9\u95f4\u8ddd\u79bb\u516c\u5f0f\u5f97\u5230\uff1aAC=\u221a[(4+4)^2+(1-7)^2]=10;AB=\u221a[(7-4)^2+(5-1)^2]=5;BC=\u221a[(-4-7)^2+(7-5)^2]=5\u221a5.\u8bbeCD=x,\u5219BD=5\u221a5-x\u3002"}, {"txt": "\u6839\u636e\u89d2\u5e73\u5206\u7ebf\u5b9a\u7406\u5f97\u5230\uff1a\u00a0\u00a0 BD/DC=AB/AC\u00a0\u00a0 \u6240\u4ee5\uff1a\u00a0\u00a0 (5\u221a5-x)/x=5/10,\u5f97\u5230\uff1ax=10\u221a5/3,\u5219CD=10\u221a5/3,BD=5\u221a5/3.\u00a0\u00a0 \u8bbeD\uff08m,n\uff09,\u56e0\u4e3aD\u5728\u76f4\u7ebfBC\u4e0a\uff0c\u5219\u6709\uff1a\u00a0\u00a0 (n-5)/(m-7)=(5-7)/[7-(-4)]\uff0c\u5373:\u00a0\u00a0 11n+2m-69=0\u00a0 \u00a02m=69-11n\u2026\u2026(1)"}, {"txt": "CD^2=x^2=500/9=(m+4)^2+(n-7)^2\u2026..(2)BD^2=125/9=(m-7)^2+(n-5)^2\u2026..(3)(3)-(2)\u5f97\u5230\uff1a\u00a0375/9=8m+14m-14n+10n+16+49-49-25\u5316\u7b80\uff1a22m-4n-9=375/9\u5c06(1)\u4ee3\u5165\u4e0a\u5f0f\u5f97\u5230\uff1a11\uff0869-n\uff09-4n-9=375/9750-125n=375/9125(6-n)=125*3/9\u6240\u4ee5n=17/3,\u8fdb\u4e00\u6b65\u5f97\u5230m=10/3. \u5373D\uff0810/3,17/3\uff09.\u5219AD\u7684\u659c\u7387k=(17/3-1)/(10/3-4)=-7.\u6240\u4ee5\u89d2\u5e73\u5206\u7ebf\u7684\u65b9\u7a0b\u4e3a\uff1ay-1=-7(x-4)\u5373\uff1a7x+y-29=0."}], [{"txt": ["\u65b9\u6cd5/\u6b65\u9aa42\uff1a\u5230\u89d2\u77e5\u8bc6\u5e94\u7528"]}, {"txt": "\u00a0 \u00a0[\u89e3\u9898\u601d\u8def]:\u5229\u7528\u5230\u89d2\u516c\u5f0f\u6c42\u51fa\u6240\u6c42\u76f4\u7ebf\u7684\u659c\u7387\uff0c\u76f4\u7ebf\u7ecf\u8fc7A\u70b9\uff0c\u7528\u70b9\u659c\u5f0f\u5373\u53ef\u5f97\u5230\u76f4\u7ebf\u65b9\u7a0b\u3002"}, {"txt": "\u76f4\u7ebfAC\u7684\u659c\u7387k1=\uff087-1\uff09/(-4-4)=-3/4\u76f4\u7ebfAB\u7684\u659c\u7387k2=(5-1)/(7-4)=4/3.\u8bbe\u2220CAD=\u2220DAB=\u2220a\uff0c\u89d2\u5e73\u5206\u7ebf\u7684\u659c\u7387=k\uff0c\u7531\u5230\u89d2\u516c\u5f0f\u5f97\u5230\uff1a(k-k2)/(1+k2\u00b7k\uff09=\uff08k1-k)/(1+k1\u00b7k\uff09\u4ee3\u5165\u6570\u503c\u5f97\u5230\uff1a(k-4/3)/(1+4k/3)=(-3/4-k)/(1-3k/4)\u5316\u7b80\u5f97\u5230\uff1a\uff083k-4\uff09^2=(4k+3)^2\u5f97\u5230\uff1ak=-7\u6216\u8005k=-1/7,\u56e0\u4e3ak