Let A(1,2), B(7,4) and C(4,−2) be the vertices of a triangle and let P(4,1) be a point in the plane.
a. (i) Find the numerical value of the area of △ABC.
b. (ii) Calculate the areas of △PAB, △PBC and △PCA.
c. (iii) Using your results, determine whether P lies inside △ABC, on its boundary, or outside it. Give suitable numerical justification.