A translation happens when a constant is summed to the coordinates of a point. We need to find the values of these constants to determine the rule of translation. When we apply the translation to the point (-9,0), the result is (-12, -4). We can rewrite this as shown below:
[tex]\begin{gathered} T(-9,0)=(-9+a,0+b)=(-12,-4) \\ -9+a=-12 \\ a=-12+9=-3 \\ 0+b=-4 \\ b=-4 \end{gathered}[/tex]The rule of translation is:
[tex]T(x,y)=(x-3,y-4)[/tex]We need to find the coordinates for the image of the point (-1, -2). Applying the rule to this point we have:
[tex]T(-1,-2)\text{ = (-1-3,-2-4)=(-4,-6)}[/tex]The image is (-4,-6).
