Jagdish has a field which is in the shape of a right angled triangle $\mathit{A}\mathit{Q}\mathit{C}$. 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 $\mathrm{O}$. Based on the above information, answer the following questions :
(i) Taking $\mathrm{O}$ as origin, coordinates of $\mathrm{P}$ are $\left(-200,0\right)$ and of $\mathrm{Q}$ are $\left(200,0\right)$. PQRS being a square, what are the coordinates of $\mathrm{R}$ and $\mathrm{S}$ ?
(ii) (a) What is the area of square PQRS ?
OR
(b) What is the length of diagonal PR in square PQRS ?
(iii) If $\mathrm{S}$ divides $\mathrm{CA}$ in the ratio $\mathrm{K}:1$, what is the value of $\mathrm{K}$, where point $\mathrm{A}$ is $\left(200,800\right)$ ?