A student lists the vertices of a triangle as P(0,0), Q(5,0) and R(0,7) in that order and obtains an area of −17.5 square units from her calculations.
(i) Recalculate the area of the triangle correctly and explain why the student’s answer carried a negative sign although the numerical value of the area is positive.
(ii) If the vertices are taken in the order Q,R,P, what signed value would the student obtain? Give reasons for your answer.
(iii) State, with justification, whether the true (unsigned) area of a triangle can ever be negative, irrespective of the order in which its vertices are listed.