question_answer

Prove that the area of a triangle with vertices \[(t,t-2),(t+2,t+2)\] and \[(t+3,t)\] is independent of t.

Answer:

Given, the vertices of a triangle \[(t,t-2),(t+2,t+2)\] and \[(t+3,t)\]

\[\therefore \] Area of the triangle \[=\frac{1}{2}|[t(t+2-t)+(t+2)(t-t+2)+(t+3)(t-2-t-2)]|\]

\[=\frac{1}{2}|(2t+2t+4-4t-12)|\]

\[=\frac{1}{2}|-8|=4\] sq. units

which is independent of t                          Hence Proved.