Show, by giving a formal construction, that the class of regular languages is closed under homomorphism. in other words, given a dfa m that recognizes b and a homomorphism f, construct a finite automaton m′ that recognizes f(b). consider the machine m′ that you constructed. is it a dfa in every case? b. show, by giving an example, that the class of non-regular languages is not closed under homomorphism.

Possible coordinates of point F are (2,-1) and (6,3).

Step-by-step explanation:

Given two triangles ABC and DEF which are congruent.

we have to find the coordinates of point F while the other are given.

A(1,0), B(-1,2), C(2,3), D(5,0), E(3,2)

Let the coordinates of F are (a,b)

By distance formula,

∵ ΔABC and ΔDEF are congruent

∴ → (1)

→ (2)

Now, we will find the value of a and b of system of equation using calculator and we get the coordinates are (2,-1) and (6,3)

Hence, possible coordinates of F are (2,-1) and (6,3).