Question

Point a (2,2) translates with the rule (x+3, y+4) to point
b. what is the diagonal distance of the translation from point a to point b?

Answer 1

   
$\displaystyle \bf\\ A(2,~2)\\ B(x+3,~y+4) \Longrightarrow B(2+3,~2+4)\Longrightarrow B(5,~6)\\ \texttt{distance }~~AB = \sqrt{\bf \Big(x_{_B}-x_{_A}\Big)^2+\Big(y_{_B}-y_{_A}\Big)^2} = \\\\ =\sqrt{\bf \Big(5-2\Big)^2+\Big(6-2\Big)^2} = \sqrt{\bf 3^2 + 4^2}=\sqrt{\bf 9 + 16}= \sqrt{\bf 25} = \boxed{\bf 5~units }$