SOLUTION
Given the question, the following are the solution steps to answer the question.
STEP 1: Write the given transformation.
[tex]\begin{gathered} (-1,-2)\Rightarrow(1,2) \\ (x,y)\Rightarrow(-x,-y) \end{gathered}[/tex]STEP 2: Describe the transformation
When we have the points transfoming as given above, this implies that there is a rotation of 180 degrees about the origin
Hence, the translation of the point to its image is given as:
Rotation of 180 degrees about the origin