Theory question 107
Coordinate Geometry(a) Find the equation of the line passing through the points (2,5) and (−4, −7).
(b) Three ships P, Q and R are at sea. The bearing of Q from P is 030° and the bearing of P from R is 300°. If |PQ| = 5 km and |PR| = 8 km, (i) illustrate the information in a diagram. (ii) calculate, correct to three significant figures, the: (I) distance between Q and R; (II) bearing of R from Q.
Show the model answer
Model answer
(a) Gradient = (−7 − 5)/(−4 − 2) = 2; y − 5 = 2(x − 2) → y = 2x + 1
(b)(i) R is on a bearing of 120° from P, so ∠QPR = 120° − 30° = 90°.
(ii)(I) QR = √(5² + 8²) = √89 ≈ 9.43 km
(II) tan∠PQR = 8/5 → ∠PQR ≈ 58.0°
Bearing of P from Q = 210°, so bearing of R from Q = 210° − 58.0° ≈ 152°
Explanation
Turn the back bearing (300° − 180° = 120°) into the bearing of R from P.