The transformation (x,y) (x+4,y-3 is performed on the segment AB.The imgae is the line segment A’B’ where point A’=(3,-3) and point B’ =(5,-3).What are the coordinates of A and B in the line segment AB

Answer: [tex]A= (-1,0)\\B=(1,0)[/tex]Step-by-step explanation: The transformation of the segment AB is: [tex](x+4,\ y-3)[/tex] Given the points of the line segment A'B': [tex]A'=(3,-3)[/tex] and  [tex]B'=(5,-3)[/tex] The coordinates of the points A and B in the line segment AB,can be calculated through this procedure: For A: x-coordinate: Substitute the x-coordinate of A' (we can represent it with[tex]x_{(A')}[/tex]) into [tex]x_{(A')}=x_A+4[/tex] and solve for [tex]x_{A}[/tex], which is the x-coordinate of A: [tex]x_{(A')}=x_A+4\\\\3=x_A+4\\\\3-4=x_A\\\\x_A=-1[/tex] y-coordinate: Substitute the y-coordinate of A' (we can represent it with[tex]y_{(A')}[/tex]) into [tex]y_{(A')}=y_A-3[/tex] and solve for [tex]y_{A}[/tex], which is the y-coordinate of A: [tex]y_{(A')}=y_A-3\\\\-3=y_A-3\\\\-3+3=y_A\\\\y_A=0[/tex] The point of A is: (-1,0) For B: x-coordinate: Substitute the x-coordinate of B' (we can represent it with[tex]x_{(B')}[/tex]) into [tex]x_{(B')}=x_B+4[/tex] and solve for [tex]x_{B}[/tex], which is the x-coordinate of B: [tex]x_{(B')}=x_B+4\\\\5=x_B+4\\\\5-4=x_B\\\\x_B=1[/tex] y-coordinate: Substitute the y-coordinate of B' (we can represent it with[tex]y_{(B')}[/tex]) into [tex]y_{(B')}=y_B-3[/tex] and solve for [tex]y_{B}[/tex], which is the y-coordinate of B: [tex]y_{(B')}=y_B-3\\\\-3=y_B-3\\\\-3+3=y_B\\\\y_B=0[/tex] The point of B is: (1,0)