ANSWER
The translation rule is
[tex]D(x,y)\rightarrow D'(x-5,y+8).[/tex]
EXPLANATION
Let [tex] \binom{x}{y} [/tex]
be the translation vector that maps [tex]D(7,-3)[/tex]
on to [tex]D'(2,5)[/tex].
Then we have the vector equation,
[tex] \binom{7}{ - 3} + \binom{x}{y} = \binom{2}{5} [/tex]
We now solve for
[tex] \binom{x}{y} [/tex]
[tex] \binom{x}{y} = \binom{2}{5} - \binom{7}{ - 3}[/tex]
This simplifies to,
[tex] \binom{x}{y} = \binom{2 - 7}{5 - - 3} [/tex]
[tex] \binom{x}{y} = \binom{2 - 7}{5 + 3} [/tex]
[tex] \binom{x}{y} = \binom{ - 5}{8} [/tex]
Therefore the translation rule is,
[tex]D(x,y)\rightarrow D'(x-5,y+8)[/tex]
