$\begin{array}{l}
a)M' = {T_{\overrightarrow v }}\left( M \right) \Leftrightarrow \overrightarrow {MM'} = \overrightarrow v \\
\Leftrightarrow \left\{ \begin{array}{l}
x' - 1 = - 3\\
y' + 4 = 4
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x' = - 2\\
y' = 0
\end{array} \right. \Rightarrow M'\left( { - 2;0} \right)\\
b)M = {T_{\overrightarrow v }}\left( {M'} \right) \Leftrightarrow \overrightarrow {M'M} = \overrightarrow v \\
\Leftrightarrow \left\{ \begin{array}{l}
1 - x' = - 2\\
- 4 - y' = 1
\end{array} \right. \Leftrightarrow \left\{ \begin{array}{l}
x' = 3\\
y' = - 5
\end{array} \right. \Rightarrow M'\left( {3; - 5} \right)\\
c)M' = {T_{\overrightarrow v }}\left( M \right) \Leftrightarrow \overrightarrow {MM'} = \overrightarrow v \\
\overrightarrow {MM'} = \left( {4 - 1;2 + 4} \right) = \left( {3;6} \right)\\
\Rightarrow \overrightarrow v = \left( {3;6} \right)
\end{array}$
