(a) Using the two- point form, \(\frac{y - y_{1}}{y_{2} - y_{1}} = \frac{x - x_{1}}{x_{2} - x_{1}}\) \(\frac{y - 5}{-7 - 5} = \frac{x - 2}{-4 - 2}\) \(\frac{y - 5}{- 12} = \frac{x - 2}{- 6}\) \(y - 5 = 2(x - 2)\) \(y - 5 = 2x - 4 \implies y - 2x = -4 + 5 = 1\) \(Equation : y = 2x + 1\) (b) (i)see figure above In \(\Delta{\text PQR,}\) (ii) (1) In \(\Delta PQR, |QR|^{2} = 5^{2} + 8^{2}\) \(25 + 64 = 89\) \(|QR| = \sqrt{89} = 9.434 km \approxeq 9.43 km\) (2) In the diagram above, the bearing of R from Q is the obtuse angle NQR. But \(\tan \alpha = \frac{8}{5} = 1.6\) \(\alpha = \tan^{-1} (1.6) = 58^\circ\) Hence, angle NQR = 360^\circ - (a + 60^\circ + 90^\circ) = 360^\circ - (58^\circ + 60^\circ + 90^\circ) = 360^\circ - 208^\circ = 152^\circ