Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables (as shown in the figure). In the field, there is a pole marked as O. Based on the above information, answer the following questions :
(i) Taking O as origin, coordinates of P are (−200,0) and of Q are (200,0). PQRS being a square, what are the coordinates of R and S ?
(ii) (a) What is the area of square PQRS ?
OR
(b) What is the length of diagonal PR in square PQRS ?
(iii) If S divides CA in the ratio K:1, what is the value of K, where point A is (200,800) ?