5 (a) P is the point (1, 7). Q is the point (5, –5). y P NOT TO SCALE O x Q (i) Find PQ . PQ = [2] f p (ii) Show that OP = OQ . [3] (iii) PQ is a chord of a circle with centre O. Calculate the circumference of this circle. ................................................. [2] (iv) PQ is the diameter of a different circle with centre R. Find the coordinates of R. ( ...................... , ...................... ) [2] © UCLES 2024 0580/41/M/J/24 11 (v) Find the equation of the perpendicular bisector of PQ. Give your answer in the form y = mx+c. y = ................................................ [4] (b) The position vector of A is a. The position vector of B is b. M is a point on AB such that AM : MB = 2 : 3. Find, in terms of a and b, the position vector of M. Give your answer in its simplest form. ................................................. [4] © UCLES 2024 0580/41/M/J/24 [Turn over 12