The line joining (P, 4) and (6, -2). Gradient: \(\frac{-2 - 4}{6 - P} = \frac{-6}{6 - P}\) The line joining (2, P) and (-1, 3) Gradient: \(\frac{3 - P}{-1 - 2} = \frac{3 - P}{-3}\) For perpendicular lines, the product of their gradient = -1. \((\frac{-6}{6 - P})(\frac{3 - P}{-3}) = -1\) \(\frac{6 - 2P}{6 - P} = -1 \implies 6 - 2P = P - 6\) \(6 + 6 = P + 2P \implies P = \frac{12}{3} = 4\)