Geometry and algebra

Question

Let there be a triangle PQR.Its vertices being P,Q,R respectively.A point A may lie either inside or on the triangle PQR.Let f(x,y)=ax+by+c. Then prove that

f(A) is less than or equal to max{ f(P),f(Q),f(R)}.Can it be solved using corner point theorem for bounded regions of linear programming

Answer 1

Hint: consider all lines of the form $ax+by+L$, where L is a real number. Hence we are done.

So yes, we can use basic ideas in linear programming.