From a point T, a man moves 12km due west and then moves 12km due south to another point Q. Calculate the bearing of T from Q.

Analyze the question: The man starts at T, goes 12 km west, then 12 km south to reach Q. We need the bearing of T from Q, which means standing at Q and looking toward T, measured clockwise from North.

Set up coordinates (East = x, North = y):

• T = (0, 0)
• After 12 km west: (−12, 0)
• After 12 km south: Q = (−12, −12)

Direction from Q to T: T − Q = (0 − (−12), 0 − (−12)) = (12, 12)

So T is 12 km east and 12 km north of Q. That is the north-east direction.

Find the angle: tan θ = 12/12 = 1, so θ = 45° from North toward East.

Bearing of T from Q = 045°

Check: The bearing of Q from T would be the back-bearing: 045° + 180° = 225°. That is option A, which is the trap. The question asks for the bearing of T from Q, not Q from T.

Tip: For "bearing of X from Y," put yourself at Y (the second point named) and look at X. Always draw a small north arrow at that point. Bearings of opposite directions differ by 180°, so you can check your answer with the back-bearing.