Mathematics

Problem

Let

D(t+1,2t-3)

E(4t,-1)

and

F(7,5)

be three points in the Cartesian plane. a. (i) Show that the area of triangle

DEF

can be written in the form

|at^2+bt+c|

, where

a

b

and

c

are constants to be determined. b. (ii) Using the result of part (i), determine all real values of

t

for which the three points are collinear.