(b) (5, 6)Let the foot of the perpendicular be M(x1, y1) Slope of line AB, i.e., y = –x + 11 = –1 Slope of line PM = \(rac{y_1-3}{x_1-2}\)Now, PM ⊥ AB⇒ \(\bigg(rac{y_1-3}{x_1-2}\bigg)\) x -1 = -1⇒ y1 –3 = x1 – 2 ⇒ x1 – y1 = –1 ...(i) Also, (x1, y1) lies on AB ⇒ x1 + y1 – 11 = 0 ⇒ x1 + y1 = 11 ...(ii) Adding (i) and (ii), we get 2x1 = 10 ⇒ x1 = 5 Putting x1 in (ii), we get y1 = 6. ∴ Required foot of the perpendicular M is (5, 6).