2009年全国各地中考数学压轴题 参考答案及评分标准（二）

101．解：（1）当t＝4－3时，四边形FBCG为正方形． ················································· 1分

当0＜t≤4时，四边形AEGD为平行四边形． ············································ 2分 （2）由题意知点D、C的坐标分别为（1），（53） ······························· 4分

∵抛物线经过原点O（0，0），∴设抛物线的解析式为y＝ax＋bx（a≠0）．

2

将D、C两点坐标代入得

a＝－ a＋b＝ 5 ·，解得 ································································· 6分

b＝63 25a＋5b＝ 5

∴抛物线的解析式为y＝－（3）存在．

3263

x＋x ··················································· 7分 55

∵点Q在抛物线上，∴点Q(x，－过点Q作QM⊥x轴于M，如图．

26x＋x

55

∵∠DAB＝60°，CD＝4，∴AB＝5． ∴S△ABQ＝

1

AB·QM 2

261

＝×5×|－x＋x|

552

12

＝|－x＋6x| ····································································· 8分 2

∵EG的延长线与抛物线交于x轴的上方 262x＋x＞0，∴－x＋63x＞0． 55

12

∴S△ABQ＝(－x＋63x)

2

∴－

∵S梯形ABCD＝

1

(CD＋AB)·BC 2

31

(4＋5)×2×

22

9＝························································································ 9分 ·2

＝

若S△ABQ＝S梯形ABCD，则

2

192

(－3x＋63x)＝． 22

整理得x－6x＋9＝0，解得x＝3． ···························································· 10分 把x＝3代入抛物线的解析式，得y＝－

692

×3＋×3＝3，即MQ555