📚 Straight Line Graphs and Coordinate Geometry | 直线图像与坐标几何
Straight line graphs are one of the most important topics in IGCSE Mathematics. They connect algebra with geometry and appear in many real-life contexts, from calculating costs to measuring speed. In this revision guide, you will learn how to plot points, calculate distance and midpoint, interpret gradient, write linear equations, and sketch lines with confidence. This topic forms the foundation for coordinate geometry, modelling, and calculus in later study.
直线图像是 IGCSE 数学中最重要的专题之一。它把代数与几何联系起来，并出现在许多实际情境中，例如计算成本或测量速度。在这份复习指南中，你将学会如何描点、计算距离和中点、理解斜率、写出直线方程，并自信地画出直线草图。这个专题为后续学习坐标几何、数学建模以及微积分打下基础。
1. The Cartesian Plane | 笛卡尔坐标系
The Cartesian plane is formed by two perpendicular number lines: the x-axis, which runs horizontally, and the y-axis, which runs vertically. They intersect at the origin, written as (0, 0). Every point is described by an ordered pair (x, y), where x gives the horizontal position and y gives the vertical position. The plane is divided into four quadrants. In the first quadrant, both x and y are positive; in the second quadrant, x is negative and y is positive; in the third quadrant, both are negative; in the fourth quadrant, x is positive and y is negative.
笛卡尔坐标系由两条互相垂直的数轴组成：x 轴水平放置，y 轴垂直放置。它们在原点相交，记作 (0, 0)。每个点用一个有序数对 (x, y) 来描述，其中 x 表示水平位置，y 表示垂直位置。整个平面分为四个象限。第一象限中 x 和 y 都为正；第二象限中 x 为负、y 为正；第三象限两者都为负；第四象限中 x 为正、y 为负。
Understanding coordinates is essential because coordinate geometry problems always rely on reading and using (x, y) values correctly. In IGCSE exams, you may be asked to identify the quadrant of a point, to plot points, or to use coordinates in distance, midpoint, and gradient calculations.
理解坐标非常重要，因为坐标几何问题始终依赖正确读取和使用 (x, y) 值。在 IGCSE 考试中，你可能会被要求判断一个点所在的象限、描出点，或者利用坐标进行距离、中点和斜率的计算。
2. Plotting Points | 描点
To plot a point such as (3, −2), start at the origin. Move 3 units to the right along the x-axis because the x-coordinate is positive, then move 2 units down because the y-coordinate is negative. Mark the point with a small cross or dot and label it clearly. Plotting points accurately is the first step in drawing straight line graphs and in solving simultaneous equations graphically.
要描出例如 (3, −2) 这样的点，请从原点开始。因为 x 坐标为正，先沿 x 轴向右移动 3 个单位；因为 y 坐标为负，再向下移动 2 个单位。用一个小叉号或圆点标出该点，并清晰地标注它。准确描点是绘制直线图像以及用图像法解联立方程的第一步。
For practice, plot the points A(2, 4), B(−3, 5), C(−4, −1) and D(5, −3). Check that each point lies in the correct quadrant: A is in quadrant I, B in quadrant II, C in quadrant III, and D in quadrant IV. Remember that the first number is always the x-coordinate and the second number is the y-coordinate.
练习时，描出 A(2, 4)、B(−3, 5)、C(−4, −1) 和 D(5, −3) 四个点。检查每个点是否位于正确的象限：A 在第一象限，B 在第二象限，C 在第三象限，D 在第四象限。请记住，第一个数字始终是 x 坐标，第二个数字始终是 y 坐标。
3. Distance Between Two Points | 两点间的距离
The distance between two points A(x₁, y₁) and B(x₂, y₂) is found by applying Pythagoras' theorem. The difference in x-coordinates gives one leg of a right
Published by TutorHao | IGCSE Mathematics Revision Series | aleveler.com
更多咨询请联系16621398022（同微信）
或截图后用「扫一扫 → 相册」选择本图