with endpoints $A\left(4,4\right)$A(4,4) and cap b times open paren 5 comma negative 1 close paren$B\left(5,-1\right)$B(5,−1) is reflected in the line y is equal to x$y=x$y=x to create its image line segment cap A prime cap b prime$\overline{A'B'}$A′B′ . Graph line segment cap A prime cap b prime$\overline{A'B'}$A′B′ . Then find the perimeter of the figure formed by the segments line segment cap A cap b$\overline{AB}$AB , line segment cap b prime cap b$\overline{B'B}$B′B , and line segment cap A cap b prime$\overline{AB'}$AB′ to the nearest tenth.