📚 Bearings and Scale Drawings | 方位角与比例绘图
In the Cambridge KS3 Mathematics course, bearings and scale drawings bring together measuring angles, using compass directions and applying ratio. A bearing is always measured clockwise from north and is written as a three-digit angle. Scale drawings use a ratio such as 1 : 25000 to shrink real distances accurately. This guide explains the essential rules, gives worked examples, and prepares you for questions such as page 287 question 2.
在剑桥 KS3 数学课程中，方位角和比例绘图将测量角度、使用罗盘方向和运用比例结合在一起。方位角总是从正北顺时针测量，并写成三位数角度。比例绘图使用如 1 : 25000 这样的比例来准确缩小实际距离。本指南解释基本规则、提供例题，并帮助你准备诸如第 287 页第 2 题的问题。
1. What Are Bearings? | 什么是方位角？
A bearing is a way of describing direction using angles. It is measured from the north line, clockwise, and must always be given as a three-figure angle. The north line is a vertical line drawn upward from a point.
方位角是用角度描述方向的一种方式。它从正北线开始按顺时针测量，并且必须始终以三位数角度表示。正北线是从某一点向上画的竖直线。
- North is 000° or 360°.
- East is 090°.
- South is 180°.
- West is 270°.
北是 000° 或 360°；东是 090°；南是 180°；西是 270°。
Bearing = angle measured clockwise from north
2. Three-Figure Bearings | 三位数方位角
If a bearing calculation gives 45°, we write it as 045° so that it has three digits. Angles less than 100° need one or two leading zeros. If an angle is exactly 360°, we write 000°. If a calculated bearing is greater than 360°, subtract 360° until the value lies between 000° and 360°.
如果方位角计算结果是 45°，我们写为 045°，使其有三位数字。小于 100° 的角度需要一位或两位前导零。如果角度正好是 360°，我们写 000°。如果计算出的方位角大于 360°，则减去 360°，直到数值在 000° 到 360° 之间。
| Calculated bearing | 计算结果 | Three-figure bearing | 三位数方位角 |
|---|---|
| 7° | 007° |
| 45° | 045° |
| 360° | 000° |
| 405° | 045° (subtract 360) |
3. Measuring Bearings in Diagrams | 在图中测量方位角
To measure the bearing of B from A, draw a north line at point A. Place the centre of the protractor at A with 0° pointing north. Measure clockwise from the north line to the line joining A to B. Always read the scale that increases clockwise from north, and write the result as three figures.
要测量从 A 到 B 的方位角，在点 A 处画一条正北线。将量角器的中心放在 A 点，0° 指向北。从正北线顺时针测量到连接 A 与 B 的直线。始终读取从北开始顺时针增加的刻度，并将结果写成三位数。
Worked example: If the line AB points to 128° on the protractor, the bearing is 128°. No further change is needed because it already has three digits.
例题：如果线段 AB 在量角器上指向 128°，则方位角为 128°。因为它已经是三位数，所以不需要进一步改变。
4. Back Bearings | 反向方位角
The back bearing is the bearing from the destination back to the starting point. If the original bearing is less than 180°, add 180°. If it is 180° or more, subtract 180°. This works because a straight line has a 180° change in direction.
反向方位角是从目的地返回起点的方位角。如果原方位角小于 180°，则加 180°。如果大于或等于 180°，则减去 180°。这是因为直线方向的改变为 180°。
ard bearing + 180°) if forward bearing < 180°; otherwise (forward bearing − 180°)
| Forward bearing | 原方位角 | Back bearing | 反向方位角 |
|---|---|
| 045° | 225° |
| 140° | 320° |
| 210° | 030° |
| 350° | 170° |
5. Scale Drawings and Scale Factors | 比例绘图与比例因子
A scale drawing shows a real object or route at a reduced or enlarged size. A scale such as 1 : 100 means 1 cm on the drawing represents 100 cm (1 m) on the ground. The scale factor is the multiplier that converts drawing lengths to real lengths.
比例绘图以缩小或放大的尺寸显示真实物体或路线。1 : 100 这样的比例表示图上的 1 cm 代表地面上的 100 cm（1 m）。比例因子是将图上长度转换为实际长度的乘数。
Real length = drawing length × scale factor
ample, on a 1 : 200 drawing, a wall drawn as 4 cm represents 4 × 200 = 800 cm = 8 m.
例如，在 1 : 200 的图中，一堵墙画成 4 cm，则实际为 4 × 200 = 800 cm = 8 m。
6. Converting Between Units on Maps | 地图上的单位换算
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