Edexcel A-Level Maths: Coordinate Geometry of Straight Lines | Edexcel A-Level 数学：直线坐标几何

📚 Edexcel A-Level Maths: Coordinate Geometry of Straight Lines | Edexcel A-Level 数学：直线坐标几何

Coordinate geometry of straight lines is a core pure mathematics topic in the Edexcel A-Level specification. It connects algebraic equations with geometric ideas such as gradient, midpoint, distance, intersection and perpendicular conditions. These skills appear regularly in both AS and A2 papers, often combined with other topics.

直线坐标几何是 Edexcel A-Level 纯数学中的核心专题。它把代数方程与斜率、中点、距离、交点和垂直条件等几何概念联系起来。这些技能在 AS 与 A2 试卷中都经常出现，并且经常与其他专题结合考查。

1. The Coordinate Plane and Straight Lines | 坐标平面与直线

A straight line in the xy-plane can be described by a linear equation in two variables, usually written in the form y = mx + c, where m is the gradient and c is the y-intercept. The line consists of all points (x, y) that satisfy the equation.

xy 平面中的直线可以用一个二元一次方程来描述，通常写作 y = mx + c，其中 m 是斜率，c 是 y 轴截距。直线由所有满足该方程的点 (x, y) 组成。

Coordinates are given as ordered pairs (x, y). The x-coordinate is measured horizontally from the origin, and the y-coordinate is measured vertically from the origin. A positive gradient means the line rises from left to right; a negative gradient means the line falls from left to right.

坐标以有序数对 (x, y) 的形式给出。x 坐标从原点水平测量，y 坐标从原点垂直测量。正斜率表示直线从左到右上升；负斜率表示直线从左到右下降。

A linear equation has variables only to the first power, so no x², xy, or y² terms appear. This is why the graph is a straight line rather than a curve.

线性方程中的变量只有一次幂，因此不会出现 x²、xy 或 y² 等项。这就是图像为直线而不是曲线的原因。

2. Gradient of a Straight Line | 直线的斜率

The gradient m between two points (x₁, y₁) and (x₂, y₂) is the ratio of vertical change to horizontal change. It is given by the formula

两点 (x₁, y₁) 与 (x₂, y₂) 之间的斜率 m 是纵向变化与横向变化之比。其计算公式为

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