Triangle RST has vertices R(−2, 2), S(1, 1), and T(−1, −3). Find the coordinates for the image of each vertex for the given rotation.R(90°, 0) (triangle RST) A. R'(−2, −2), S'(−1, 1), and T'(3, −1) B. R'(−2, 2), S'(1, −2), and T'(3, 1) C. R'(2, 2), S'(−1, −1), and T'(1, −3) D. R'(−2, 2), S'(1, −1), and T'(3, 1)

Answer:A. [tex]R'(-2,-2),S'(-1,1),[/tex] and [tex]T'(3,-1)[/tex]Step-by-step explanation:Given:Vertices of triangle RST are [tex]R(-2,2),S(1,1),[/tex] and [tex]T(-1,-3)[/tex].Rotation is 90° about the center O(0,0). The rotation is counter-clockwise as the angle of rotation is positive.Now, the co-ordinate rule for 90° rotation counter-clockwise is given as:[tex](x,y)[/tex] → [tex](-y,x)[/tex][tex]x[/tex] and [tex]y[/tex] values interchange their places with [tex]y[/tex] becoming negative when interchanged.So, [tex]R(-2,2)[/tex] → [tex]R'(-2,-2)[/tex] [tex]S(1,1)[/tex] → [tex]S'(-1,1)[/tex] [tex]T(-1,-3)[/tex] → [tex]T'(-(-3),-1)[/tex] ⇒[tex]T(-1,-3)[/tex] → [tex]T'(3,-1) [/tex]Therefore, the image of the vertices are [tex]R'(-2,-2),S'(-1,1),[/tex] and [tex]T'(3,-1)[/tex].