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多点运动问题是动态几何题中的一种重要题型,在近年各地中考试卷中屡有出现。这类试题由于多个质点的运动,停留在不同位置,形成不同的图形,往往需要分类讨论,稍有不慎,就容易漏解。现列举两例,略作说明。一、以直角三角形为载体,考查分类讨论思想例1如图1,在Rt△ABC中,∠C=90°,AC=4 cm,BC=3 cm。动点M、N从点C同时出发,均以每秒1 cm的速度分别沿CA、CB向终点A、B移动,同时动点P从点B出发,以每秒2 cm的速度沿BA向终点A移动,连接PM、PN,设移动时间为t(单位:
The problem of multi-point movement is an important type of question in dynamic geometry. It has appeared frequently in examination papers in various places in recent years. Due to the movement of multiple particles in such questions, stay in different locations, forming different graphics, often need to discuss the classification, a little careless, it is easy to leak. Now cite two cases, a little explanation. First, the right triangle as the carrier, examines the classification of thinking Example 1 Figure 1, in Rt △ ABC, ∠ C = 90 °, AC = 4 cm, BC = 3 cm. The moving points M and N start at the same time from point C and move along CA and CB to end points A and B respectively at the speed of 1 cm per second. At the same time, moving point P starts from point B and travels at a speed of 2 cm per second End point A move, connect PM, PN, set the movement time t (unit: