Answer: The co-ordinates of the points A and B are (-1, 0) and (1, 0) respectively.
Step-by-step explanation: Given that the following transformation is applied on the line segment AB and the image is a line segment A'B', where point A'= (3,-3) and point B' = (5,-3).
(x, y) ⇒ (x+4, y-3).
We are to find the coordinates of A and B in line segment AB.
Let, the co-ordinates of points A and B be (a, b) and (c, d) respectively.
So, we have
(a, b) ⇒ (a+4, b-3) = (3, -3),
(c, d) ⇒ (c+4, d-3) = (5, -3).
This implies that
[tex]a+4=3~~~\Rightarrow a=3-4~~~\Rightarrow a=-1,\\\\b-3=-3~~~\Rightarrow b=-3+3~~~\Rightarrow b=0,\\\\c+4=5~~~\Rightarrow c=5-4~~~\Rightarrow c=1,\\\\d-3=-3~~~\Rightarrow d=-3+3~~~\Rightarrow d=0.[/tex]
Thus, the co-ordinates of the points A and B are (-1, 0) and (1, 0) respectively.
