The vertices of a triangular plot of land are A(−3,−1), B(5,2) and C(1,7). Two pegs are driven into the ground at points Q(2,3) and R(3,5).
a. (i) Compute the area of △ABC.
b. (ii) For the point Q, find the areas of △QAB, △QBC and △QCA, and hence decide whether Q lies inside, on an edge of, or outside the triangular plot.
c. (iii) Repeat part (ii) for the point R.
d. (iv) Compare the locations of Q and R with respect to △ABC, clearly stating your conclusions.