让我们一起来探索平面直角坐标系中平行四边形的顶点的坐标之间的关系.第一步:数轴上两点连线的中点表示 如图,在平面直角坐标系中,平行四边形ABC0的顶点O在原点,...
\u8ba9\u6211\u4eec\u4e00\u8d77\u6765\u63a2\u7d22\u5e73\u9762\u76f4\u89d2\u5750\u6807\u7cfb\u4e2d\u5e73\u884c\u56db\u8fb9\u5f62\u7684\u9876\u70b9\u7684\u5750\u6807\u4e4b\u95f4\u7684\u5173\u7cfb\u3002\u7b2c\u4e00\u6b65\uff1a\u6570\u8f74\u4e0a\u4e24\u70b9\u8fde\u7ebf\u7684\u4e2d\u70b9\u8868\u793a\u7b2c\u4e00\u6b65\uff1a 1 \u7b2c\u4e8c\u6b65\uff1a \u7b2c\u4e09\u6b65\uff1a \u6216 X 1 +x 3 =x 2 +x 4 y 1 +y 3 =y 2 +y 4 \uff0c \u7684\u548c\u76f8\u7b49\u3002 \u89e3\uff1a\u7b2c\u4e00\u6b65\uff1a\u6545\u7b54\u6848\u4e3a\uff1a1\uff0c\u5982\u56fe\uff1a \uff0e\u89e3\uff1a\u2235MN\u662f\u68af\u5f62AEFB\u7684\u4e2d\u4f4d\u7ebf\uff0cAE\u2225BF\uff0c\u2234E\u3001F\u7684\u6a2a\u5750\u6807\u5206\u522b\u662fx 1 \uff0cx 2 \uff0c \u89e3\uff1a\u7531\u7b2c\u4e09\u6b65\u63a8\u51fax 1 +x 3 =x 2 +x 4 y 1 +y 3 =y 2 +y 4 \uff0c\u6545\u7b54\u6848\u4e3a\uff1ax 1 +x 3 =x 2 +x 4 y 1 +y 3 =y 2 +y 4 \uff0c\u7684\u548c\u76f8\u7b49\uff0e\u753b\u51fa\u6570\u8f74\u5373\u53ef\u6c42\u51fa\u7b2c\u4e00\u6b65\uff1b\u5148\u6c42\u51faN\u662fEF\u4e2d\u70b9\uff0c\u6c42\u51faN\u7684\u6a2a\u5750\u6807\uff0c\u6839\u636e\u68af\u5f62\u7684\u4e2d\u4f4d\u7ebf\u6027\u8d28\u6c42\u51fa\u7eb5\u5750\u6807\u5373\u53ef\uff1b\u6839\u636e\u5e73\u884c\u56db\u8fb9\u5f62\u6027\u8d28\u63a8\u51faQ\u662fAC\u548cBD\u7684\u4e2d\u70b9\uff0c\u6839\u636e\u4ee5\u4e0a\u7ed3\u8bba\u5373\u53ef\u6c42\u51fa\u7b54\u6848\uff0e
\uff081\uff09\u65b9\u7a0bx2-4=0\u7684\u4e24\u6839\u4e3ax1=2\uff0cx2=-2\uff0c\u6240\u4ee5a=-2\uff0cb=2\uff0c\u6240\u4ee5A\u70b9\u7684\u5750\u6807\u4e3a\uff08-2\uff0c0\uff09\uff0cB\u70b9\u7684\u5750\u6807\u4e3a\uff080\uff0c2\uff09\uff0c\u6839\u636eOA\u2225BC\u4e14OA=BC\u53ef\u5f97C\u70b9\u5750\u6807\u4e3a\uff082\uff0c2\uff09\uff1b\uff082\uff09\u2460A\uff08-2\uff0c0\uff09\uff0cB\uff080\uff0c2\uff09\uff0c\u53ef\u77e5\u2220BAO=\u2220C=45\u00b0\uff0c\u2235OA\u2225BC\uff0c\u2234\u2220OBC=90\u00b0\u2220COB=45\u00b0\uff0c\u5c06\u5e73\u884c\u56db\u8fb9\u5f62\u7ed5O\u70b9\u9006\u65f6\u9488\u65cb\u8f6c\uff0c\u4f7fOC\u843d\u5728Y\u8f74\u4e0a\uff0c\u6b63\u597d\u65cb\u8f6c\u7684\u662f45\u00b0\uff0c\u2220EDO=\u2220BOC=45\u00b0\u2234DE\u2225OC\uff0e\u2461\u65cb\u8f6c\u524d\u540e\u4e24\u4e2a\u5e73\u884c\u56db\u8fb9\u5f62\u91cd\u53e0\u90e8\u5206\u662f\u76f4\u89d2\u68af\u5f62\uff0cOA=2\uff0cOH=2\uff0cAH=HG=2-2\uff0cOB=2\uff0c\u6240\u4ee5S=12\uff082-2+2\uff09?2=22-1\uff0e
第一步:故答案为:1,如图:.解:∵MN是梯形AEFB的中位线,AE∥BF,
∴E、F的横坐标分别是x1,x2,
由第一步得出:N和M的横坐标是:
x1+x2 |
2 |
AE+BF |
2 |
y1+y2 |
2 |
故答案为:M(
x1+x2 |
2 |
y1+y2 |
2 |
解:与第二步解法类似,根据平行四边形的性质得出QA=QC,QB=QD,推出:(
x1+x3 |
2 |
y1+y3 |
2 |
x2+x4 |
2 |
y2+y4 |
2 |
故答案为:(
x1+x3 |
2 |
y1+y3 |
2 |
x2+x4 |
2 |
y2+y4 |
2 |
解:由第三步推出x1+x3=x2+x4 y1+y3=y2+y4,
故答案为:x1+x3=x2+x4 y1+y3=y2+y4,和相等.
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