The original point is:
[tex]A(6,-12)[/tex]The first step will be to identify the x and y values:
[tex]\begin{gathered} x=6 \\ y=-12 \end{gathered}[/tex]And the second step will be to apply the given rule.
The rule for the transformation is:
[tex](x,y)\longrightarrow(x-4,y+7)[/tex]This tells us that to find the image point we have to subtract 4 to the x value and add 7 to the y value.
We apply the rule to the original point:
[tex](6,-12)\longrightarrow(6-4,-12+7)[/tex]And solving the operations:
[tex](6,-12)\longrightarrow(2,-5)[/tex]We have found the image point:
[tex]A^{\prime}(2,-5)[/tex]Answer:
[tex]A^{\prime}(2,-5)[/tex]