We have to apply transformations to point A=(3,5).
First, we have to rotate 270° counterclockwise, which is the same to rotate 90° clockwise, so the transformation is:
[tex]\begin{gathered} (x,y)\to(-y,x) \\ \text{For point A(3,5) the rotation is:} \\ A(3,5)\to A^{\prime}(-5,3) \end{gathered}[/tex]
Then transtalate by the rule T(2,2), this means:
[tex]\begin{gathered} T_{(2,2)}(x,y)=(x+2,y+2) \\ So,\text{ for point A'(-5,3):} \\ A^{\doubleprime}=T_{(2,2)}(-5,3)=(-5+2,3+2)=(-3,5) \end{gathered}[/tex]
Finally we have a reflection on x-axis, so:
[tex]\begin{gathered} (x,y)\to(x,-y) \\ \text{For point A''(-3,5):} \\ A^{\doubleprime}(-3,5)\to A^{\doubleprime}^{\prime}(-3,-5) \end{gathered}[/tex]
The final point after all the transformations is A'''(-3,-5)
