Respuesta :
In order to find the coordinates of the preimage A, B and C, we need to go backwards in the transformations (that is, from A"B"C" to A'B'C', then from A'B'C' to ABC)
The tranformation from A'B'C' to A"B"C" is a reflection over the y-axis, that is, it causes a change in the x-coordinate signal.
So in order to find the coordinates of A'B'C', we need to undo this reflection:
[tex]\begin{gathered} A^{\doubleprime}(-2,-1)\to A^{\prime}(2,-1) \\ B^{\doubleprime}(0,3)\to B^{\prime}(0,3) \\ C^{\doubleprime}(4,1)\to C^{\prime}(-4,1) \end{gathered}[/tex]Now, the transformation from ABC to A'B'C' is a dilation by a scale factor of 1/3. In order to undo this, we need to apply the inverse dilation from A'B'C' to ABC, that is, a dilation by a scale factor of 3:
[tex]\begin{gathered} A^{\prime}(2,-1)\to A(2\cdot3,-1\cdot3)=A(6,-3) \\ B^{\prime}(0,3)\to B(0\cdot3,3\cdot3)=B(0,9) \\ C^{\prime}(-4,1)\to C(-4\cdot3,1\cdot3)=C(-12,3) \end{gathered}[/tex]So the coordinates of the preimage are A(6, -3), B(0, 9) and C(-12, 3).
