Final answer:
To create a scale drawing from point P to Q, 8km away at a 110° bearing, use a scale factor (1cm = 2km), and draw a 4cm line from P at a 110° angle clockwise from North. The drawing accurately represents the distance and bearing on paper.
Step-by-step explanation:
To create a scale drawing with a bearing, you must first understand how to properly represent both the magnitude and direction of your vector, which in this case is the distance from point P to point Q. Since we are given a scale of 1cm/2 km, we must convert the real distance (8 km) to a scaled distance on our drawing.
- Determine the scale: Our scale is 1cm to represent 2 km. Therefore, for 8 km, you would draw a line that is 4 cm long (since 8 km divided by 2 km/cm equals 4 cm).
- Identify the reference direction: Follow the convention of using North as a reference direction for bearing, which means you'll start from the northern point of your compass or protractor.
- Measure the bearing angle: Use a protractor to measure a 110° angle clockwise from the North point. The bearing of 110° tells us that our line must be drawn at this angle relative to North.
Now, to actually draw the vector on your paper:
- Position the protractor's origin at point P and rotate it so that the 0° mark aligns with the north direction on your page, which is typically the upward direction if your page orientation is standard.
- Mark a point at 110° on the protractor, ensuring this is the angle clockwise from North.
- From point P, draw a straight line through the mark you've made on the protractor, and measure this line to be 4 cm in length to represent the 8 km distance at your chosen scale. Point Q will be at the end of this 4 cm line.
Using this method, you've now accurately represented the distance and bearing from point P to point Q on your scale drawing.