In order to identify the transformations, first let's write the coordinates of each point:
[tex]\begin{gathered} A(-6,8)\to A^{\prime}(6,-8)_{} \\ B(-6,2)\to B^{\prime}(6,-2)_{} \\ C(1,2)\to C^{\prime}(-1,-2) \\ D(1,8)\to D^{\prime}(-1,-8) \end{gathered}[/tex]
We can see that the coordinates of A, B, C and D changed the signals of x and y:
[tex](x,y)\to(-x,-y)[/tex]
This means the transformation is a reflection about the origin.
Another way of transforming ABCD into A'B'C'D would be a reflection about the point (-2.5, 5), which is the center of ABCD, and then a translation of 5 units right and 10 units down.
