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题目:定长为9的线段AB的两个端点在抛物线y~2=x上移动,记线段AB的中点为M。求M到y轴的最短距离,并求此时点M的坐标。这是今年高考题(理、工、农、医类)第八题,这道题有一定的坡度。此题虽系一成题,由于解法较多,思路较宽,所以也是一道考知识,考能力的好题。这道压卷题,无疑地,也是数学单科得高分的关键。但是根据笔者参加阅卷所收集到的信息看,考生对此题的得分情况是很不理想的。下面我们给出此题标准答案以外的多种解法,以供大家参考。
Title: The two endpoints of the segment AB with a fixed length of 9 move on the parabola y~2=x, and the midpoint of the segment AB is M. Find the shortest distance from M to the y-axis, and find the coordinates of the point M at this time. This is the eighth item of this year’s college entrance examination (physics, engineering, agriculture, medicine). This topic has a certain degree of slope. Although this question is a one-point question, because of more solutions and broader ideas, it is also a good question for the examination of knowledge and examination ability. This scroll question is, without doubt, the key to high scores in mathematics. However, according to the information collected by the author when he participated in the marking, the candidate’s score on this topic is very unsatisfactory. Below we give a variety of solutions in addition to the standard answer to this question for your reference.