Plot the points P(−2,1), Q(3,1) and R(3,5) on the Cartesian plane and answer the following:
a. (i) Join the points in the order P–Q–R to form a triangle PQR. Provide a neat, labelled sketch.
b. (ii) Prove that △PQR is right-angled at Q using the positions of the vertices with respect to the axes.
c. (iii) Determine the area of △PQR in square units.
d. (iv) Calculate the length of the side PR using an appropriate theorem and hence find the perimeter of the triangle.