Bearings and Scale Drawings | 方位角与比例绘图

📚 Bearings and Scale Drawings | 方位角与比例绘图

Bearings are used in navigation and map reading to describe the direction of one point from another. In Cambridge KS3 Mathematics, you need to measure, draw and calculate three-figure bearings, and use scale drawings to solve real-life distance and direction problems.

方位角用于导航和地图判读，用来描述一个点相对于另一个点的方向。在剑桥 KS3 数学中，你需要测量、绘制和计算三位数方位角，并利用比例绘图解决现实生活中的距离与方向问题。

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1. What Are Bearings? | 什么是方位角？

A bearing is a direction measured clockwise from the north line. It is always written as a three-figure number, so north is 000°, east is 090°, south is 180° and west is 270°.

方位角是从正北方向线按顺时针方向测量的角度。它总是写成三位数形式，因此正北是 000°，正东是 090°，正南是 180°，正西是 270°。

Bearings do not use compass points such as ‘north-east’ in final answers. The angle must be given in degrees from 000° to 360°.

方位角的最终答案不使用 ‘东北’ 这类罗盘方位点，而必须用 000° 到 360° 之间的度数表示。

For example, north-east is exactly halfway between north and east, so its bearing is 045°. South-west is halfway between south and west, so its bearing is 225°.

例如，东北方向正好在正北和正东之间，因此它的方位角是 045°。西南方向在正南和正西之间，因此它的方位角是 225°。

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2. Three-Figure Bearing Rules | 三位数方位角规则

• Always measure from the north line. 始终从正北线开始测量。
• Always turn clockwise. 始终按顺时针方向旋转。
• Always write the answer with three digits, e.g. 045° not 45°. 答案始终写成三位数，例如写 045° 而不是 45°。

If a bearing is less than 100°, place a zero in front. If it is less than 10°, place two zeros in front.

如果方位角小于 100°，在前面加一个零；如果小于 10°，则加两个零。

The three-figure rule prevents confusion between directions such as 5° and 50°. Writing 005° and 050° makes the order of magnitude clear.

三位数规则可以避免混淆像 5° 和 50° 这样的方向。写成 005° 和 050° 能清楚地表示角度的大小。

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

To measure the bearing of point B from point A, first draw a clear north line at A. Then place the protractor with its centre at A and 000° pointing north.

要测量点 B 相对于点 A 的方位角，先在 A 点画一条清晰的正北线，然后把量角器的中心放在 A 点，并使其 000° 指向正北。

Read the angle clockwise from the north line to the line AB. If the line points to the left, you may need to measure the smaller angle and subtract from 360°.

从正北线沿顺时针方向读角到直线 AB。如果直线指向左侧，你可能需要先测量较小的角，再用 360° 减去它。

For example, if the protractor shows 40° from north clockwise, the bearing is 040°. If the line AB points north-west, the small angle from north to the line is 45° anticlockwise, so the bearing is 360° − 45° = 315°.

例如，如果量角器显示从正北顺时针 40°，则方位角为 040°。如果直线 AB 指向西北，从正北到该直线的小角是逆时针 45°，因此方位角为 360° − 45° = 315°。

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4. Scale Drawings and Maps | 比例绘图与地图

A scale drawing represents a real object or distance using a fixed ratio. A map scale such as 1 : 50 000 means that 1 cm on the map represents 50 000 cm (or 500 m) on the ground.

比例绘图用固定的比例表示实际物体或距离。地图比例尺如 1 : 50 000 表示地图上的 1 cm 代表实际地面的 50 000 cm（即 500 m）。

Scale can be written as a ratio (1 : n), as a statement (1 cm to 5 km) or as a bar scale.

比例尺可以写成比（1 : n）、文字说明（1 cm 代表 5 km）或线段比例尺。

Scale | 比例尺	1 cm on map | 图上 1 cm
1 : 25 000	25 000 cm = 0.25 km
1 : 100 000	100 000 cm = 1 km
1 : 2 500 000	2 500 000 cm = 25 km

Always convert units carefully: 100 000 cm = 1 km. If the scale is given as ‘1 cm to 5 km’, then 1 cm represents 500 000 cm, so the ratio is 1 : 500 000.

务必仔细换算单位：100 000 cm = 1 km。如果比例尺写作 ‘1 cm 代表 5 km’，那么 1 cm 代表 500 000 cm，因此比是 1 : 500 000。

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5. Converting Real Distances to Map Distances | 实际距离与图上距离的换算

To find the map distance, divide the real distance by the scale factor after converting to the same units.

求图上距离时，先将实际距离换算成相同单位，再除以比例尺的倍数。

Map distance = Real distance ÷ Scale factor

图上距离 = 实际距离 ÷ 比例尺倍数

For example, a real distance of 5 km on a scale of 1 : 250 000 is first converted to 500 000 cm. Then divide by 250 000 to get 2 cm on the map.

例如，实际距离 5 km 在 1 : 250 000 的比例尺下，先换算成 500 000 cm，再除以 250 000，得到图上距离 2 cm。

To find the real distance, multiply the map distance by the scale factor.

求实际距离时，将图上距离乘以比例尺的倍数。

Real distance = Map distance × Scale factor

实际距离 = 图上距离 × 比例尺倍数

Example: On a 1 : 100 000 map, two villages are 3.5 cm apart. The real distance is 3.5 × 100 000 = 350 000 cm = 3.5 km.

例子：在一张 1 : 100 000 的地图上，两个村庄相距 3.5 cm。实际距离为 3.5 × 100 000 = 350 000 cm = 3.5 km。

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6. Using Bearings to Plot a Journey | 用方位角绘制航行路线

A journey can be represented by drawing lines

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