2023 AISS AM S3 EOY Q7

The diagram shows a triangle \({PQR}\) and \({\angle PRQ = 90^\circ}\).

The coordinates of \({P}\), \({Q}\) and \({R}\) are \({(-7, 2)}\), \({(4, 7)}\) and \({(m, -m)}\) respectively, where \({m}\) is a constant.

1. Show that \({m = 1}\).[2]
2. \({PQRS}\) is a parallelogram. Find the coordinates of \({S}\).[2]
3. \({T}\) is the point on \({PR}\) such that \({PT : TR = 1 : 3}\).
   Find the coordinates of \({T}\).[2]
4. Find the area of the triangle \({PTQ}\).[2]