2009年中考数学专题复习 - 压轴题(6)

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在Rt△BB?H中，B?H?BH?12BB??23，

························································· 12分 ?23) ·3B?H?6，?OH?3，?B?(?3，设直线B?F的解析式为y?kx?b

?3??23??3k?b?k???6??43 解得?

33?k?b???b??3???236332?y?x? ··············································································································· 13分

3??y??3x?3x???3710???? 解得 ?M，???333?77103x??y???y??，62??7??3 ????3103??在直线AC上存在点M，使得△MBF的周长最小，此时M?，． ·········· 14分 ???7?7??解法二：

过点F作AC的垂线交y轴于点H，则点H为点F关于直线AC的对称点．连接BH交········································· 11分 AC于点M，则点M即为所求．

过点F作FG?y轴于点G，则OB∥FG，BC∥FH．

??BOC??FGH?90，?BCO??FHG

?y ??HFG??CBO

0)． 同方法一可求得B(3，A O C M G F H 图10 ?B x

在Rt△BOC中，tan?OBC?33，??OBC?30，可求得GH?GC?33，

?GF为线段CH的垂直平分线，可证得△CFH为等边三角形， ?AC垂直平分FH．

?53?即点H为点F关于AC的对称点．?H?0，?3?? ······················································· 12分 ???设直线BH的解析式为y?kx?b，由题意得

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5?k?3?0?3k?b???9 解得? 5?3?b???b??533??3??y?593?53··············································································································· 13分 3 3?55x???3x?3?3710??y?93 解得? ?M?，????77??y??103?y??3x?3??7??3 ????3103??在直线AC上存在点M，使得△MBF的周长最小，此时M?，． 1 ???7?7??18.(2008年沈阳市)如图所示，在平面直角坐标系中，矩形ABOC的边BO在x轴的负半轴上，边OC在y轴的正半轴上，且AB?1，OB??3，矩形ABOC绕点O按顺时针方向

旋转60后得到矩形EFOD．点A的对应点为点E，点B的对应点为点F，点C的对应点为点D，抛物线y?ax?bx?c过点A，E，D． （1）判断点E是否在y轴上，并说明理由； （2）求抛物线的函数表达式；

（3）在x轴的上方是否存在点P，点Q，使以点O，B，P，Q为顶点的平行四边形的面积是矩形ABOC面积的2倍，且点P在抛物线上，若存在，请求出点P，点Q的坐标；若不存在，请说明理由．

y E A B 18. 解：（1）点E在y轴上理由如下：

连接AO，如图所示，在Rt△ABO中，?AB?1，BO?3，?AO?2

2F C D O

x ··················································· 1分

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?sin?AOB?12，??AOB?30

??由题意可知：?AOE?60

??BOE??AOB??AOE?30?60?90

?点B在x轴上，?点E在y轴上． ··················································································· 3分

???（2）过点D作DM?x轴于点M ?OD?1，?DOM?30

12??在Rt△DOM中，DM??点D在第一象限，

，OM?32

?31?点D的坐标为?，?22?? ····································································································· 5分 ???由（1）知EO?AO?2，点E在y轴的正半轴上

?点E的坐标为(0，2)

?点A的坐标为(?3，1) ······································································································· 6分 ?抛物线y?ax?bx?c经过点E，

2?c?2

1)，D?由题意，将A(?3，?31，?22??2代入y?ax?bx?2中得 ???8??3a?3b?2?1a???9?? 解得 ?3?31b?2??a??b??53?422?9?892?所求抛物线表达式为：y??x?539x?2 ································································ 9分

（3）存在符合条件的点P，点Q． ··················································································· 10分 理由如下：?矩形ABOC的面积?AB?BO?3

?以O，B，P，Q为顶点的平行四边形面积为23．

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由题意可知OB为此平行四边形一边， 又?OB?3

·············································································································· 11分 ?OB边上的高为2·

2) 依题意设点P的坐标为(m，?点P在抛物线y??89x?2539x?2上

??89m?2539m?2?2

解得，m1?0，m2??538

?53?，2? ?P1(0，2)，P2????8???以O，B，P，Q为顶点的四边形是平行四边形，

?PQ∥OB，PQ?OB??当点P1的坐标为(0，2)时，

3，

y E A B F C D x O M 点Q的坐标分别为Q1(?3，2)，Q2(3，2)； 当点P2的坐标为?????53?，2?时， ?8????1338?，2?，Q4??点Q的坐标分别为Q3???33?，2?． ······················································· 14分 ??8???（以上答案仅供参考，如有其它做法，可参照给分）

19.(2008年四川省巴中市) 已知：如图14，抛物线y??与直线y??34x?b相交于点B，点C，直线y??3434x?3与x轴交于点A，点B，

2x?b与y轴交于点E．

（1）写出直线BC的解析式．

（2）求△ABC的面积．

（3）若点M在线段AB上以每秒1个单位长度的速度从A向B运动（不与A，B重合），同时，点N在射线BC上以每秒2个单位长度的速度从B向C运动．设运动时间为t秒，请写出△MNB的面积S与t的函数关系式，并求出点M运动多少时间时，△MNB的面积最大，最大面积是多少？

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19. 解：（1）在y????34x?3?0

234x?3中，令y?0

2?x1?2，x2??2

?A(?2，0)，B(2，0) ······················································ …… 此处隐藏：950字，全部文档内容请下载后查看。喜欢就下载吧 ……