Goal and prerequisites
Use a consistent reference direction, convert a map scale and interpret displacement magnitudes and ratios. Review vectors transformations before starting.
Method and its conditions
Measure bearings clockwise from north and write three digits. A reverse bearing differs by 180° modulo 360°. Convert map lengths using the stated scale before changing units. Vector magnitude uses Pythagoras; scalar multiples indicate parallel directions.
Worked example: show the decisions
If B is on bearing 065° from A, A is on bearing 245° from B. A 4 cm map distance at scale 1: 25000 represents 100000 cm=1 km. A displacement vector(6,8) has magnitude 10; its components are not its length.
Contrast: diagnose an incorrect approach
The reverse bearing is not 360° minus the original bearing. A negative scalar reverses a vector’s direction, while a positive scalar preserves it. Equal magnitudes alone do not imply parallel vectors. Coordinates describe points; subtract them to obtain a displacement.
Transfer: try a changed situation
A=(2,3), B=(14,21) and P=(6,9). Find the fraction AP/AB along the segment, and justify collinearity.
Transfer solution and interpretation
AB=(12,18) and AP=(4,6)=AB/3. Thus AP/AB=1/3 and P lies on the same line between A and B. The equal positive scalar in both components is the key evidence.
The bearing of B from A is 030°. What is the bearing of A from B, in degrees?
- Reverse direction by adding 180°, reducing modulo 360° if needed.
- Using the stated quantities: 180+30 = 210.
- Check the domain, units and whether the answer is an exact value, bound or estimate.
Compare the other answer choices
Keep the original forward bearing.
Subtract the forward angle from 180° instead of adding it.
Reflect across north instead of reversing the direction.
Try it, then explain it.
Complete a short set without looking at the example. After each answer, explain which operation preserved the relationship and why the result makes sense.
Sources & authorship
Original Slope explanations and examples. References support the concepts; they are not the source of copied questions. Independent educator review is pending.
0580 syllabus for exams in 2025–2027