Mastering Bearings and Scale Drawings | 掌握方位与比例图

📚 Mastering Bearings and Scale Drawings | 掌握方位与比例图

Bearings and scale drawings are essential tools for describing directions and representing real-world distances on paper. Whether you are navigating at sea, reading a map, or solving geometry problems, these skills help you work accurately with angles and proportions. This revision guide covers everything you need to master bearings and scale drawings at the Cambridge KS3 level.

方位与比例图是描述方向和在纸上表示实际距离的基本工具。无论是海上导航、读地图还是解决几何问题，这些技能都能帮助你准确处理角度和比例。本复习指南涵盖你在剑桥 KS3 阶段需要掌握的方位与比例图全部内容。

1. What Are Bearings? | 什么是方位？

A bearing is a way of describing direction using angles. It is always measured clockwise from north, and it is expressed as a three-figure number. For example, due east is written as 090°, not 90°.

方位是用角度描述方向的一种方法。它始终从正北开始顺时针测量，并用三位数表示。例如，正东方写作 090°，而不是 90°。

Bearings are used in navigation, surveying, and map reading because they provide a precise and unambiguous direction. The three-figure format avoids confusion between angles such as 5° and 50°.

方位用于导航、测量和地图阅读，因为它们提供了精确且无歧义的方向。三位数格式避免了如 5° 和 50° 这样的角度之间的混淆。

2. Measuring Bearings with a Protractor | 用量角器测量方位

To measure a bearing, place the protractor on the point where you are starting, with the 0° mark pointing true north. Measure clockwise to the line joining the two points and read the angle. Always check that your reading is between 000° and 360°.

要测量一个方位，把量角器放在起点，让 0° 刻度指向正北。顺时针测量到连接两点的直线，并读取角度。务必确认你的读数在 000° 到 360° 之间。

If the angle is less than 100°, add leading zeros to make it a three-figure bearing, such as 045° for northeast. This standard notation is vital in Cambridge exams.

如果角度小于 100°，在前面加零使其成为三位数，如东北方向写作 045°。这种标准表示在剑桥考试中至关重要。

3. Three-Figure Bearings | 三位数方位

Every bearing must be given as three digits. For example, north is 000° or 360°, east is 090°, south is 180°, and west is 270°. Intermediate directions follow the same rule: southeast is 135°, northwest is 315°.

每一个方位都必须以三位数给出。例如，正北是 000° 或 360°，正东是 090°，正南是 180°，正西是 270°。中间方向遵循相同规则：东南是 135°，西北是 315°。

When you measure an angle of 7°, write 007°. This ensures no confusion with 070° or 700°. In practical navigation, three-figure bearings are used worldwide.

当你测得 7° 的角度时，要写作 007°。这确保不会与 070° 或 700° 混淆。在实际导航中，全世界都使用三位数方位。

4. Bearings from One Point to Another | 点到点的方位

To find the bearing of point B from A, imagine standing at A and facing north. Turn clockwise until you face B directly. The angle you turn is the bearing from A to B. Draw a north line at A and measure carefully.

要找出从点 A 到点 B 的方位，想象自己站在点 A 面朝正北，然后顺时针转动直至正对点 B。你转过的角度就是从 A 到 B 的方位。在点 A 画出指北线并仔细测量。

Label the north line clearly and use a sharp pencil for accuracy. Often, you will be given a diagram and must calculate the bearing by subtracting angles from 360° or using properties of parallel lines.

清晰地标出指北线，用尖铅笔以保证准确性。通常你会拿到一个图，需要通过从 360° 中减去角度或利用平行线的性质来计算方位。

5. Return Bearings | 返回方位

The return bearing is the direction from B back to A. You can find it by adding 180° to the original bearing if it is less than 180°, or subtracting 180° if it is 180° or more. This gives the opposite direction.

返回方位是从点 B 返回点 A 的方向。如果原方位小于 180°，则加 180°；如果大于等于 180°，则减 180°。这样便得到相反方向。

For example, if the bearing from A to B is 065°, the return bearing is 065° + 180° = 245°. If it is 210°, then 210° − 180° = 030°. Always write the answer as three figures.

例如，若从 A 到 B 的方位是 065°，返回方位为 065° + 180° = 245°。如果是 210°，则 210° − 180° = 030°。答案必须始终写作三位数。

6. Introduction to Scale Drawings | 比例图简介

A scale drawing represents real objects or distances in a smaller, proportional size. The scale tells you how lengths on the drawing relate to actual lengths. For instance, a scale of 1 : 100 means 1 cm on paper stands for 100 cm (1 m) in reality.

比例图是用较小的比例尺寸表示真实物体或距离的图形。比例告诉你图上的长度如何与实际长度对应。例如，比例 1 : 100 表示纸上 1 厘米代表实际 100 厘米（1 米）。

Scales are written as a ratio, like 1 : 50 000, or as a statement, such as ‘1 cm represents 0.5 km’. Understanding scale is essential for map reading and technical drawing.

比例写作比值形式，如 1 : 50 000，或写成语句“1 厘米代表 0.5 千米”。理解比例对于地图阅读和工程制图必不可少。

7. Choosing an Appropriate Scale | 选择合适的比例尺

When creating a scale drawing, pick a scale that fits your page and is easy to work with. For instance, if the real distance is 10 km, using a scale of 1 cm to 1 km results in a 10 cm line—manageable on A4 paper.

在绘制比例图时，选择一个适合纸张且易于换算的比例。例如，实际距离为 10 千米，用 1 厘米代表 1 千米的比例会画出 10 厘米线——在 A4 纸上很方便。

Avoid scales that give awkward measurements, like 1 cm to 3 m if you need to draw 10 m, as it would give 3.33 cm. Simpler ratios reduce errors in exams.

避免选择导致古怪尺寸的比例，如 1 厘米代表 3 米，而你需要画 10 米，则会得出 3.33 厘米。较简单的比例在考试中能减少错误。

8. Converting Between Map and Actual Distances | 地图与实际距离的转换

To find the actual distance, multiply the map length by the scale factor. If the scale is 1 : 20 000, a 5 cm measurement on the map corresponds to 5 cm × 20 000 = 100 000 cm = 1 km.

要计算实际距离，将地图长度乘以比例因子。若比例为 1 : 20 000，图上 5 厘米对应实际 5 cm × 20 000 = 100 000 cm = 1 千米。

Actual distance = map distance × scale factor

实际距离 = 地图距离 × 比例因子

When the scale is given as a statement, e.g., ‘1 cm to 5 km’, use unit conversions carefully. Always express your final answer in the required unit, often metres or kilometres.

当比例以语句形式给出时，例如“1 厘米代表 5 千米”，要仔细换算单位。最终答案始终以要求的单位表示，通常是米或千米。

9. Drawing a Scale Diagram | 绘制比例图

Begin by setting up the scale and calculating all needed lengths. Draw a baseline with a ruler, and mark key points according to given bearings or distances. Use a protractor to draw angles precisely.

首先确定比例并计算所有需要的长度。用直尺画一条基线，并根据给定的方位或距离标出关键点。用量角器精确画出角度。

Label each point clearly and indicate the scale on the drawing. For combined bearing-scale problems, draw north lines at appropriate points and measure bearing angles clockwise from north.

清晰地标注每一个点，并在图上标明比例。对于方位与比例结合的题目，在相应点处画出指北线，并从正北顺时针测量方位角。

Double-check your measurements: even a 1 mm error in a scaled drawing can represent a large real-world distance.

仔细检查你的测量：比例图中哪怕 1 毫米的误差都可能代表真实世界中很大的距离。

10. Solving Problems with Bearings and Scales | 用方位和比例解题

Many KS3 problems ask you to locate a point given its distance and bearing from another point. On a scale diagram, start at the known point, draw the north line, mark the bearing, then measure the scaled distance along that direction.

许多 KS3 题目要求根据某点给出另外一点的距离和方位来定位。在比例图上，从已知点开始，画指北线，标出方位，然后沿着该方向量出比例距离。

For example, a ship leaves port and sails 8 km on a bearing of 070°, then 5 km on a bearing of 160°. To find the final position, draw a scale diagram, carefully plotting each leg of the journey.

例如，一艘船从港口出发，沿 070° 方位行驶 8 千米，再沿 160° 方位行驶 5 千米。要找到最终位置，画出比例图，仔细绘制每段航程。

Using the diagram, you can then measure the return bearing and distance back to the start, giving a complete navigational solution.

利用该图，你便可测量返回起点的方位和距离，得到完整的导航解答。

11. Common Mistakes and Tips | 常见错误与技巧

One frequent mistake is measuring the bearing anticlockwise instead of clockwise. Always double‑check that your protractor is aligned with north as 0° and that you read the clockwise value.

一个常见错误是逆时针测量方位而不是顺时针。务必反复确认量角器的 0° 对准正北，并且读取的是顺时针值。

Another error is forgetting to write bearings as three figures. Even if the angle is 30°, you must write 030°. In scale drawings, misreading the scale or units can lead to completely wrong distances.

另一个错误是忘记将方位写作三位数。即使角度是 30°，也必须写作 030°。在比例图中，读错比例或单位会得出完全错误的距离。

Always start at the correct point and draw a thin north line.
始终从正确的点开始，画一条细细的指北线。
Convert all distances to the same unit before using the scale.
在使用比例前把所有距离换算为相同单位。
To check a bearing, see if a rough sketch matches the three-figure value (e.g., 230° should point roughly southwest).
要检查方位，看粗略草图是否符合三位数值（例如，230° 应大致指向西南）。

12. Summary and Practice | 总结与练习

Bearings are three‑figure angles measured clockwise from north; scale drawings use ratios to shrink real sizes proportionally. Mastering these concepts allows you to interpret maps, solve construction problems, and handle real‑world navigation tasks.

方位是从正北顺时针测量的三位数角度；比例图利用比值将实际尺寸按比例缩小。掌握这些概念能让你读懂地图、解决作图问题并处理真实世界的导航任务。

To strengthen your skills, practise measuring bearings with a protractor, calculating return bearings, and creating scale diagrams from written descriptions. The more you draw, the more confident you will become.

为了加强技能，请练习用量角器测量方位、计算返回方位，并根据文字描述绘制比例图。你画得越多，就会越自信。

Published by TutorHao | Mathematics Revision Series | aleveler.com

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Mastering Bearings and Scale Drawings | 掌握方位与比例图