SAT数学英文教程之Lines and Distance

2014年05月16日17:07 来源：小站整理: 参与（0）阅读（3427）

摘要：SAT是由美国大学委员会委托美国教育测验服务社定期举办的测验，做为美国各大学申请入学的重要参考条件之一。SAT中的数学部分包括数字与运算，代数与方程，几何，统计学，概率，数据分析。希望这份珍贵的英文原版教程能够帮助更多备考SAT的同学。

虽然中国考生的基础教育，特别是在数学部分，在全世界范围内都是数一数二的，所以对于中国SAT考生来说，SAT数学部分与其他项目相比也相对比较低。但是如果备考SAT的同学对SAT数学部分掉以轻心，很有可能造成失分悲剧。官方真题Official为备考SAT的同学们找到了英文原版SAT教程，希望对同学们有所帮助。

Lines and distance are fundamental to coordinate geometry, not to mention to the Math IC test. Even the most complicated coordinate geometry question uses the concepts covered in the next few sections.

Distance Measuring distance in the coordinate plane is made possible thanks to the Pythagorean theorem. If you are given two points, (x1,y1), and (x2,y2), their distance from each other is given by the following formula:

The diagram below shows how the Pythagorean theorem plays a role in the formula. The distance between two points can be represented by the hypotenuse of a right triangle whose legs are lengths (x2 – x1) and (y2 – y1).

To calculate the distance from (4, –3) to (–3, 8), plug the coordinates into the formula:The distance between the points is , which equals approximately 13.04. You can double-check this answer by plugging it back into the Pythgorean theorem.Finding Midpoints The midpoint between two points in the coordinate plane can be calculated using a formula. If the endpoints of a line segment are (x1, y1) and (x2, y2), then the midpoint of the line segment is:In other words, the x- and y-coordinates of the midpoint are the averages of the x- and y-coordinates of the endpoints.Here’s a practice question:What is the midpoint of the line segment whose endpoints are (6, 0) and (3, 7)?　　To solve, all you need to do is plug the points given into the midpoint formula . x1 = 6, y1 = 0, x2 = 3, and y2 = 7.

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