For a triangle with vertices

MATHEMATICS · Multi-part · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

A(x_1,y_1)

B(x_2,y_2)

and

C(x_3,y_3)

answer the following: (i) Write the algebraic expression that gives the area of

\triangle ABC

directly in terms of the six coordinates. (ii) Explain why this expression is zero when the three points are collinear. (iii) If the coordinates are

A(2,5)

B(-1,-3)

and

C(4,1)

, calculate the numerical value of the expression obtained in part (i) and hence state the area of the triangle.