<u><em>Answer:</em></u>
D' ..................> (-2,2)
C'' .................> (3,-1)
A''' ................> (4,-2)
B'' .................> (4,2)
<u><em>Step-by-step explanation:</em></u>
<u>Before we begin, we should remember the rotation rules:</u>
<u>1- Rotation 90° clockwise:</u>
Coordinates (x,y) become (y,-x)
<u>2- Rotation 90° counter clockwise:</u>
Coordinates (x,y) become (-y,x)
<u>3- Rotation 180° clockwise:</u>
Coordinates (x,y) become (-x,-y)
<u>4- Rotation 270° counter clockwise:</u>
Coordinates (x,y) become (y,-x) ...........> same as rotation 90° clockwise
<u>Now, let's consider the given problem:</u>
<u>1- Coordinates of D' if polygon ABCD rotates 90° counter clockwise to create A'B'C'D'</u>
Original coordinates of point D are (2,2)
Rotation 90° counter clockwise means that the new coordinates will be (-y,x) which is (-2,2)
<u>2- Coordinates of C'' if polygon ABCD rotates 90° clockwise to create A''B''C''D''</u>
Original coordinates of point C are (1,3)
Rotation 90° clockwise means that the new coordinates will be (y,x) which is (3,-1)
<u>3- Coordinates of A''' if polygon ABCD rotates 180° clockwise to create A'''B'''C'''D'''</u>
Original coordinates of point A are (-4,2)
Rotation 180° clockwise means that the new coordinates will be (-x,-y) which is (4,-2)
<u>4- Coordinates of B'' if polygon ABCD rotates 270° counter clockwise to create A''B''C''D''</u>
Original coordinates of point B are (-2,4)
Rotation 270° counter clockwise means that the new coordinates will be (y,-x) which is (4,2)
Hope this helps :)
