Answer:
The correct option is B.
Step-by-step explanation:
The vertices of preimage are L(2,-2), M(4,-2), N(1,-3) and O(5,-3).
The vertices of image are L'(-3,-2), M'(-3,-4), N'(-4,-1) and O'(-4,-5).
The relationship between preimage and image is defined as
[tex](x,y)\rightarrow (y-1,-x)[/tex]
In option A, 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left.
If a figure rotated 90-degree counterclockwise, then
[tex](x,y)\rightarrow (-y,-x)[/tex]
Translation 1 unit to the left,
[tex](x,y)\rightarrow (-y-1,-x)[/tex]
Therefore option A is incorrect.
In option B, 270-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left.
[tex](x,y)\rightarrow (y-1,-x)[/tex]
Therefore option B is correct.
In option C, a translation 1 unit to the left followed by a 270-degree counterclockwise rotation about the origin.
[tex](x,y)\rightarrow (y,-(x-1))[/tex]
Therefore option C is incorrect.
In option D, a translation 1 unit to the left followed by a 90-degree counterclockwise rotation about the origin.
[tex](x,y)\rightarrow (-y,x-1)[/tex]
Therefore option D is incorrect.
