Answer: (2,9)
Explanation:
Given: A point (9,-1) is first translated by rule [tex]T_{-4,3}: (x,y) \to (x-4, y+3)[/tex] followed by rotation of 270° .
Rule of rotation of 270° :[tex](x,y)\to (y,-x)[/tex]
Image of (9,-1) after translation:
[tex](9,-1)\to (-9,-1+3)= (-9,2)[/tex]
Then, image after rotation of 270° : [tex](-9,2)\to (2,9)[/tex]
Hence, the image point of (9,-1)(9,−1) after the transformation [tex]T_{-4,3}[/tex] and rotation of 270° is (2,9).
