City Q is at a distance of 12 km to the south of city P. City R is 13 km to the north-west of city Q and west of city P. City S is 24 km to the south of city R. How far is city S from city Q and in which direction from it? MCQ with Answer and Explanation

Let P be (0,0). Q is (0,-12). R is West of P, so R is (x, 0). Distance R to Q is 13. By Pythagoras, x² + (-12)² = 13² -> x² + 144 = 169 -> x² = 25 -> x = -5 (West). So R is at (-5, 0). S is 24km South of R, so S is at (-5, -24). Distance from Q(0,-12) to S(-5,-24) -> Δx = -5, Δy = -12. Distance = √((-5)² + (-12)²) = 13km. S is West and South of Q